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Study 27 Exact Nuclear Scattering

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Study 27 — Exact nuclear scattering

Charter published 2026-08-26. Corpus not yet ingested. Law drafted here, to be frozen verbatim at corpus stage before any scoring.

The field's own measured surprise

In December 2025 a three-institution team — W. Horiuchi (Osaka Metropolitan University; NITEP; RIKEN Nishina Center), Y. Suzuki (Niigata University; RIKEN Nishina Center), and R. B. Wiringa (Physics Division, Argonne National Laboratory) — posted a pair of companion papers computing high-energy nuclear scattering without truncating the multiple-scattering series: Glauber-theory calculations of high-energy nuclear scattering observables using variational Monte Carlo wave functions (arXiv:2512.20095, submitted 23 Dec 2025, report NITEP 271, "to appear in Phys. Rev. Lett") and Glauber-theory analysis of nuclear reactions on 12C target with variational Monte Carlo wave functions (arXiv:2512.20100, 22 pages, 21 figures, report NITEP 272, "to appear in Phys. Rev. C") — VERIFIED, both arXiv abstract pages and both full texts live-fetched 2026-08-26. The journal versions are reported published in Physical Review Letters on 2026-05-18 (DOI 10.1103/ppqx-yn59) and Physical Review C on 2026-06-01 (DOI 10.1103/gcbk-s7tc) — REPORTED via the phys.org coverage ("Exact calculations sharpen view of atomic nuclei," August 2026); the APS landing pages returned 403 to automated fetch this session, so the two 10.1103 DOIs carry the REPORTED tag on this page.

What they computed: elastic differential cross sections and total reaction cross sections for p+12C, 4He+12C, 6He+12C, and 12C+12C, with Glauber's phase-shift function evaluated by Monte Carlo integration "up to all orders of nucleon-nucleon multiple scatterings" — no truncation — over variational Monte Carlo (VMC) wave functions generated from the realistic Argonne v18 two-nucleon and Urbana X three-nucleon potentials; the 12C wave function is the starting point of a Green's function Monte Carlo calculation whose ground-state energy is −93.3(0.4) MeV (all VERIFIED, sentences grepped verbatim from the live-downloaded arXiv full texts, 2026-08-26).

What they found is the shear this study charters:

  • The continuum approximation overestimates, by a printed integer band. "The cumu-1 approximation overestimates σ_R by 30–50 mb beyond 300 MeV/nucleon, while the cumu-2 almost reproduces the full calculation" (12C+12C total reaction cross sections; cumu-1 is the first-cumulant approximation, equivalent to the optical-limit approximation, OLA) — VERIFIED, quoted from 2512.20095v2 full text, fetched 2026-08-26.
  • The full discrete calculation agrees with the data. The full calculation reproduces the 12C+12C interaction cross sections "accurately measured at 400-1000 MeV/nucleon" — the papers' word is "excellently" — VERIFIED, same fetch.
  • On the halo nucleus the gap is largest. For 6He+12C (a two-neutron-halo projectile), "The Full calculation reproduces one interaction cross section datum very well" near 800 MeV/nucleon, where σ_R ≈ σ_I holds because 6He has no bound excited state, while "The OLA or cumu-1 approximation overestimates the cross section considerably" — VERIFIED, same fetch. The papers give the 6He overestimate no single number, only "considerably" and their figures; this page prints none.
  • Elastic shape parts company at a named momentum transfer. cumu-1 tracks the full calculation only up to roughly the second diffraction minimum at q ≈ 1.5 fm⁻¹ "and then deviates largely at larger q values"; cumu-2 "show[s] reasonable agreement with Full calculations up to the backward angles" — VERIFIED, quoted from 2512.20100v2, fetched 2026-08-26.
  • The authors' own verdict: "The OLA does not work well, however, especially for reactions involving a halo nucleus," and the cumulant expansion of the phase-shift function "converges rapidly up to the second order for the above systems" — VERIFIED, both quoted from the fetched full texts.

The experimental anchor behind the halo story is forty years old and sits in a public archive under an exact accession. I. Tanihata et al., Phys. Rev. Lett. 55(24), 2676 (1985) measured interaction cross sections for the lithium isotope chain at 790 MeV/nucleon at the Bevalac; the 11Li-on-carbon row is EXFOR subentry E1174013: REACTION (6-C-0(3-LI-11,ABS),,SIG), DATA = 1040 mb, DATA-ERR = 60 mb, EN = 8.69×10⁹ eV (790 MeV/nucleon × A = 11), with a 0.3 PER-CENT scattering-out systematic in ERR-1 — VERIFIED, both the raw X4 record and the computational CSV fetched live from nds.iaea.org, 2026-08-26. The anomalously large cross section was later read as a two-neutron halo: a deduced 11Li rms matter radius of 3.27 ± 0.24 fm against ~2.5 fm for 6–9Li, with a two-neutron separation energy of 315 ± 50 keV (radius and separation energy read from the live-fetched Bertulani Physics of Radioactive Beams lecture-notes PDF, 2026-08-26 — VERIFIED at that source; the underlying primary tables not independently re-fetched).

So the field's own published position, as of mid-2026, is this: Glauber multiple-scattering theory admits a full discrete multi-nucleon evaluation and a continuum "optical-limit" shortcut that smears the discrete nucleons into a one-body density — "It has often been employed because μ₁(b) is obtained from the one-body densities of the projectile and target nuclei" (VERIFIED, quoted from the fetched full text) — and where nuclei are exotic, the shortcut's predictions diverge from measurement while the full discrete calculation agrees. That finding is the field's, published in the field's own journals with the field's own numbers. This study does not add to it. This study builds a replay court around it.

Section zero — the discrimination gate

Before any physics is graded, the instrument must be shown able to fail. A divergence meter that reads large on every nuclide — halo and well-bound alike — is a turn counter, not a court, and the program has retired an instrument for exactly that defect before. Every integer in this gate is frozen here, in the charter, before any corpus byte is read, with one declared exception: the two pair energies that must come from archive rows not yet pinned (the 6He and 11Be rows of arm 3) are pinned — accession plus archival date suffix — at corpus stage, before the gate runs and before any D is evaluated, under the S5 discipline. The minted configuration sets are bound the same way: the generator's integer seed is frozen in this charter (the minted-rails clause names it), the generator's specification and every checksum are published before any D is evaluated, and a regeneration is a new fact on this page, never a replacement. None of it moves after scoring. A FAIL is published as a FAIL.

The score, frozen verbatim. For projectile P on 12C at scoring energy E, the court evaluates the same frozen discrete pipeline (defined in the crossings below) twice — once as the full all-orders product over the presented configurations, once as the first-cumulant (optical-limit) exponential — and prints

D(P, E) = q(σ_OLA) − q(σ_Full), a signed integer in millibarns, where q is the frozen floor-to-integer-mb quantisation (Crossing B). Both arms read the identical presented configuration sets, the identical frozen profile-function rail, the identical impact-parameter lattice, and the identical truncated-exponential rule. Nothing differs between the arms except the object the field says differs: all orders versus first cumulant.

The four arms, in scoring order:

  1. Always-green control (scored first). A_P = A_T = 1: one nucleon on one nucleon. The generating polynomial G(b, λ) = ⟨∏(1 − λΓ)⟩ has degree A_P·A_T = 1 in λ (the degree identity VERIFIED from Eq. 47 of the fetched 2512.20100v2), so the first cumulant is the complete sum, algebraically, and D = 0 exactly on every machine. This case is constructed to pass certainly. If it prints anything but 0, the harness is broken — the study halts on an instrument defect, and no physics is scored.
  2. Replication arm. 12C+12C at the three frozen energies 400, 550, 800 MeV/nucleon: D must land inside the field's own printed band, 30 ≤ D ≤ 50, at each of the three. The band is the papers' "30–50 mb beyond 300 MeV/nucleon" (VERIFIED above), adopted as a frozen integer window. If the court's exact replay cannot reproduce the one divergence the field printed as integers, the instrument is void and every downstream criterion is void with it.
  3. Discrimination arm. Three size-matched pairs, each halo projectile against a well-bound projectile of the same mass number, all on 12C: (6He, 6Li), (11Li, 11B), (11Be, 11B). Each pair is scored at one frozen energy — the halo member's pinned EXFOR-row energy in integer keV per nucleon (Crossing C) — and both members of a pair run at that same energy, so the D-difference measures halo structure, never energy dependence. The governing 11Li row is declared here: E1174013 at 790 MeV/nucleon (E1262002 and the low-energy rows are corpus anchors, not the gate's energy source). The governing 6He and 11Be rows carry no accession on this page yet; they are pinned — accession plus archival date suffix — at corpus stage, before the gate runs and before any D is evaluated, under S5. PASS requires D(halo) − D(partner) ≥ M = 30 mb at the pair's frozen energy, for all three pairs; a pair whose halo row prints ROW_ABSENT is VOID and published as VOID, and if fewer than two pairs survive, this arm is VOID and the study is void at charter stage. 11B serves both A = 11 halos; that reuse is declared here, not discovered later.
  4. Control ceiling. N = 8 well-bound control projectiles on 12C — 4He, 6Li, 7Li, 9Be, 10B, 11B, 13C, 16O — scored with the identical pipeline, every one at the single frozen control energy E = 800 MeV/nucleon, declared here so no control energy is chosen after a D is visible. If more than K = 2 of the 8 print D > 60 mb, the instrument does not reproduce the approximation's known behaviour on nuclei where the field says it behaves, it therefore has no discriminating power, and the study is void at charter stage — published as void, with the eight integers on the page. A control struck by CONFIG_ABSENT leaves the denominator, and the ceiling adjusts by the frozen rule K = ⌊N/4⌋ over the surviving N; if fewer than 6 controls survive, this arm is VOID and the study is void with it.

The controls are the healthy population, and they are the arm that makes the gate falsifiable: a pipeline artifact that inflates D everywhere fails the ceiling; a pipeline that deflates D everywhere fails the replication band; a pipeline that cannot tell 6He from 6Li fails the discrimination margin. Three independent ways to be voided on the page before a single claim is made.

The two readings and where they disagree

Reading What it holds constant The observation that separates it Sourcing
Continuum optical limit — the nucleus is its one-body density; scattering is the first cumulant of a smear The density profile (a size and a shape-of-average) Overestimates 12C+12C σ_R by 30–50 mb beyond 300 MeV/nucleon; overestimates the 6He+12C cross section "considerably"; elastic prediction deviates "largely" beyond q ≈ 1.5 fm⁻¹. The smear keeps the magnitude scale and loses the appointment. VERIFIED — all three quoted from the arXiv full texts fetched 2026-08-26
Full discrete multi-scattering — the nucleus is a set of correlated nucleon coordinates; scattering is the all-orders product over the A_P·A_T nucleon pairs The identity of the configuration: which nucleon pairs, at which impact parameters, with which correlations Reproduces the 12C+12C interaction cross sections measured at 400–1000 MeV/nucleon "excellently"; reproduces the single 6He+12C datum "very well" near 800 MeV/nucleon; the second cumulant already agrees "up to the backward angles." The configuration keeps the appointment the density cannot. VERIFIED — same fetch
The null — the exact-vs-approximation divergence this court measures is a pipeline artifact (profile quantisation, lattice choice, truncated exponential), not a signature of discreteness Nothing; it predicts size-matched well-bound controls diverge as much as halos This is what Section zero exists to test, and it is not a straw man: every crossing in this court is a quantisation that could, if botched, manufacture divergence. The null is retired only by the gate — the replication band, the discrimination margin, and the control ceiling together — never by citation. Design statement of this charter

The adversary is separated on shape, never magnitude. The optical limit is not the adversary because its cross sections are the wrong size — over most of the chart they are nearly the right size, which is why it served for decades. It is the adversary because it has no configuration identity: it answers every question about which nucleons scattered where with a density average, and on nuclei whose few outermost nucleons sit far from the core, the average is the wrong object. Two neutrons at large radius are an appointment; a smeared tail is a magnitude.

The court and its exact keys

This study speaks only in exact string keys and exact integers, on archives the public already owns. Every load-bearing archive claim below was verified by live fetch on 2026-08-26.

The claim class, stated verbatim: "A presented configuration is verified; an unknown scattering amplitude is not searched." The court replays presented discrete nucleon configurations through a frozen algebraic pipeline and grades the printed integers against published cross sections. It derives no wave function, fits no potential, and predicts no unmeasured experiment.

Nuclide keys

A nuclide on this court is the exact triple (Z, A, element symbol) as printed by NUBASE2020/AME2020. The mass rail is the AME2020 atomic-mass column, whose fixed decimal places make every value an exact scaled integer with no float required — the file prints micro-amu to three decimals, so the court stores nano-amu integers. The halo anchor row, read live from the file on 2026-08-26 (VERIFIED):

Key AME2020 value (as printed) Court integer
(3, 11, Li) mass excess 40728.259 ± 0.615 keV 40,728,259 ± 615 eV
(3, 11, Li) atomic mass 11 043723.581 ± 0.660 micro-u 11,043,723,581 ± 660 nano-u
(3, 11, Li) binding energy / A 4155.3817 ± 0.0559 keV 41,553,817 ± 559 deci-eV

NUBASE2020 line 78 for the same nuclide (VERIFIED, file fetched 2026-08-26): mass excess 40728.3 ± 0.6 keV, half-life 8.75 ± 0.06 ms, Jπ 3/2−*, year of discovery 1966, branches B−=100, B−n=86.3(9)%, B−2n=4.1(4)%, B−3n=1.9(2)%, B−α=1.7(3)%, B−d=0.0130(13)%, B−t=0.0093(8)%.

Cross-archive agreement was measured, not assumed — and it is not uniform. The IAEA LiveChart API row for the same nuclide returns mass excess 40728.259 ± 0.615 keV, matching the AME2020 file digit for digit, but half-life 8.75 ± 0.14 ms against NUBASE2020's ± 0.06 ms (the API row's ENSDF publication cut-off is 1-Jan-2011; extraction date 2026-08-26) — both sides VERIFIED, fetched live 2026-08-26. Any criterion touching a value that differs between evaluations names which archive it freezes.

EXFOR accession keys

Experimental data enter the court only by EXFOR accession: a 5-character entry ID plus 3-digit subentry, e.g. E1174013 (subentry 001 of every entry is the bibliographic block; data subentries 002+ each carry one REACTION code and one DATA table — VERIFIED, read from the raw X4 retrieval of E1174, 2026-08-26). The anchor accessions this charter names for the corpus stage, all resolved live on 2026-08-26 (VERIFIED except as marked):

Accession Reaction / quantity Value as served Reference
E1174013 6-C-0(3-LI-11,ABS),,SIG 1040 ± 60 mb at EN 8.69×10⁹ eV (790 MeV/nucleon) I. Tanihata et al., PRL 55(24) 2676 (1985)
E1262002 6-C-0(3-LI-11,ABS),,SIG 1047 ± 40 mb at 790 MeV/nucleon I. Tanihata et al., PLB 206(4) 592 (1988)
E2012005 6-C-0(3-LI-11,ABS),,SIG 1 point at EN ≥ 4.40×10⁹ eV I. Tanihata et al., PLB 287(4) 307 (1992)
E2437003 6-C-12(3-LI-11,NON),,SIG 1938 ± 70 mb (3.41×10⁸ eV) and 1774 ± 45 mb (4.40×10⁸ eV) T. Moriguchi et al., PRC 88 024610 (2013)
C1148002 · O1334009 · D0473002/004/006 elastic DA · charge-changing SIG · fragment-production SIG indexed for corpus stage Kolata 1992 · Blank 1992 · Simon 2007

Two remembered numbers failed against the live archives, and the failures are recorded as keys-discipline evidence: the often-quoted 11Li+C value "1060 ± 10 mb" is served by neither Tanihata entry (the archives return 1040 ± 60 and 1047 ± 40 — both VERIFIED 2026-08-26), and the Horiuchi PRL prints its PLB 206, 592 reference with year 1985 where the standard year is 1988 (discrepancy noted; neither silently copied). An archive fetched beats a number remembered.

The archives

Source URL Format / keys Version / cadence Auth Sourcing
EXFOR web + API https://nds.iaea.org/exfor/ — search x4list?Target=…&Reaction=…&json, retrieval x4get?DatasetID=…&op=csv&plus=1 (computational CSV), x4get?sub=<ENTRY|SUBENT>[:YYYYMMDD] (raw X4; date suffix = archival version), plus=5 (X5 JSON) Entry+subentry accessions; REACTION codes; DATA tables in printed decimal Continuously refreshed — update feed updated/x4upd.js reported last_updated="2026-08-26" (same-day) and CountOfEntry = 25,823; every entry retrievable at any archival date None — anonymous GET VERIFIED — all four retrieval modes exercised live 2026-08-26
AME2020 mass table https://www-nds.iaea.org/amdc/ame2020/mass_1.mas20.txt Fixed-width Fortran (format string in-file); N−Z, N, Z, A, symbol, mass excess (keV), binding/A, β-decay energy, atomic mass (micro-u); # marks estimated values, * non-calculable Versioned static publication — 472,648 bytes as fetched 2026-08-26; in-file stamp 3 Mar 2021; published Chin. Phys. C 45 030002/030003 (2021); prior evaluations hosted alongside None VERIFIED — full file downloaded and byte-counted live
NUBASE2020 https://www-nds.iaea.org/amdc/ame2020/nubase_4.mas20.txt Fixed-width; (Z, A) keys, mass excess, half-life, Jπ, discovery year, decay branches Same versioned publication — 761,906 bytes as fetched 2026-08-26 None VERIFIED — full file downloaded live
IAEA LiveChart API https://nds.iaea.org/relnsd/v1/data?fields=ground_states&nuclides=11li CSV rows; charge radius, moments, separation energies, mass excess Regenerated same-day (Extraction_date 2026-08-26); ENSDF cut-off per row None VERIFIED — row fetched live 2026-08-26
NNDC ENSDF archivals https://www.nndc.bnl.gov/ensdfarchivals/ Versioned zips ensdf_YYMMDD_NNN.zip; dataset DOI 10.18139/nndc.ensdf/1845010 Page dates 2022-02-14 and 2026-06-01 None VERIFIED reachability + listing (fetched 2026-08-26); internal 80-column card format REPORTED

The declared crossings

Three crossings into exactness exist, each at its own site, each performed once. After them the court is rational products, rational sums, and integer comparison, end to end.

  • Crossing A — published parameters and coordinates → exact rationals. Profile-function parameters (σ_NN^tot, α, β at each frozen energy, from the published tables of the pinned papers) and presented configuration coordinates arrive as printed decimal strings and are read once, at load, into exact rationals whose denominator is the printed power of ten. No binary float representation is constructed at any point. The Gaussian profile Γ_NN is then evaluated once onto the frozen impact-parameter lattice (b = 0 to B_max = 20 fm in steps of 1/100 fm) with the frozen truncated-exponential rule below, and published as a checksummed profile rail before any scoring.
  • Crossing B — exact rational cross sections → integer millibarns. σ values are quantised once, at the seal, by floor to integer mb. The lattice sum σ = Σ 2πb Δb [1 − |e^{iχ(b)}|²] over the frozen lattice is the sealed object — not the continuum integral it discretises — and it is a finite rational sum, identical on every machine, because π never enters as an irrational: the court freezes π as the named exact rational π_rail = 245850922/78256779 (a continued-fraction convergent of π, frozen here, printed and checksummed with the profile rail), so every lattice weight 2·π_rail·b·Δb is one frozen rational, identical in every arm. All arms run the identical lattice, the identical profile rail, the identical frozen weights, and one frozen exponential rule: the degree-64 truncated Taylor sum in exact rationals. The arms are one pipeline at three truncations of one object. Writing X(b) for the pair-profile sum Σ Γ over one presented configuration: the Full arm seals the exact all-orders configuration average ⟨∏(1 − Γ)⟩ over the presented sets; the cumu-1 (OLA) arm seals the degree-64 exponential of −μ₁(b), with μ₁(b) = ⟨X(b)⟩ the exact rational configuration mean; the cumu-2 arm seals the degree-64 exponential of −μ₁(b) + μ₂(b)/2, with μ₂(b) = ⟨X(b)²⟩ − ⟨X(b)⟩² the exact rational configuration variance — the first two cumulants of the same generating polynomial G(b, λ) whose degree identity anchors the always-green control. No third estimator, no second lattice, no separate rounding: S3 is decidable from this paragraph and Crossing A alone. Section zero's replication arm exists to show this pipeline reproduces the field's own printed band before anything else is graded.
  • Crossing C — EXFOR fields → court integers. DATA and DATA-ERR in barns convert to integer mb by exact ×1000 on the printed string (1.04 b → 1040 mb); EN fields convert to integer keV per nucleon by the printed-string rule with the subentry's own A. Scoring energies for halo rows are these integers, never a rounded convenience.

The minted rails, named because they are not archive bytes. Two inputs are minted by this program rather than fetched: the profile rail (Crossing A) and the configuration sets — the discrete nucleon-coordinate samples the court replays. Published VMC configurations are not distributed as public files (the papers name their generation method — Metropolis sampling, ~50% acceptance, 500,000 configurations for 4He, 200,000 for 6He, 40,000 for 12C, with production runs generally using 40,000 per nucleus — VERIFIED, quoted from the fetched 2512.20100v2). The corpus-stage configuration sets are therefore produced by a deterministic generator whose integer seed is frozen in this charter: seed = 20260826. The generator's full specification and every set's checksum are published before any D is evaluated — no divergence integer exists, publicly or privately, before the generator is public — and a regeneration (a new seed, a revised generator) is published as a new fact on this page beside the old checksums, never as a replacement. Each set is checksummed and published before scoring; a nuclide whose configuration set cannot be sourced or deterministically generated is recorded CONFIG_ABSENT and excluded from both arms — absence and zero are different answers, and no absent set is folded in as a nil contribution.

The program's reading — coordinates and rigid bonds

Attributed as the program's reading, and only that: what the field calls the full multiple-scattering calculation is, structurally, what this program calls a court of exact coordinates and bonds — each nucleon an exact lattice coordinate, the strong-force binding that holds a configuration together a set of rigid bonds, and the scattering observable a finite combinatorial object over the A_P·A_T pair bonds (a degree-144 generating polynomial, for carbon on carbon) whose evaluation in exact arithmetic yields one string on every machine. The optical limit is, in the program's vocabulary, a magnitude adversary: it replaces the bonded configuration with its density average and keeps only the size. The halo nucleus is where the program's thesis and the field's measurement coincide — two neutrons bonded at large radius are an appointment that a smear cannot keep, and the field measured the miss in millibarns.

The analogy motivates a decidable test — the gate, the pairs, the bands, the integers above. The test is what gets sealed. The analogy never is.

What the full quantum calculation still requires

This court replays a frozen algebraic pipeline. The physics that makes the pipeline's inputs meaningful is quantum many-body theory, and this study computes none of it:

  • Wave functions. The correlated configurations come from variational Monte Carlo solutions of realistic two- and three-nucleon potentials (Argonne v18 + Urbana X — VERIFIED from the fetched texts); producing them is a major computation the papers ran on Argonne Laboratory Computing Resource Center and Argonne Leadership Computing Facility machines under an INCITE grant (VERIFIED, acknowledgment quoted from the fetched texts). The court consumes configurations; it cannot generate physical ones.
  • Amplitudes and phases. The Glauber phase-shift function rests on the eikonal (straight-line) and adiabatic (frozen-nucleon) approximations — R. J. Glauber, in Lectures in Theoretical Physics, Vol. 1, p. 315 (Interscience, 1959; citation VERIFIED from the papers' reference lists). The court inherits both approximations wholesale and grades nothing about their validity.
  • Energy dependence. The nucleon-nucleon profile parameters are energy-dependent fits to nucleon-nucleon scattering data; the court freezes the published table and computes no dependence beyond it.
  • Coulomb and breakup. The papers include Coulomb breakup through cutoff impact parameters b_C = 6.07 fm (12C+12C), 5.53 fm (6He+12C), 4.89 fm (4He+12C), 3.03 fm (p+12C) — VERIFIED, values grepped from the fetched 2512.20100v2. The court adopts these as frozen rationals; it derives none of them.

Nothing on this page claims quantum scattering theory is wrong, that probability amplitudes are defective, or that this court replaces Monte Carlo simulation or the supercomputers that produced the wave functions. The claim is narrower and it is exactly three sentences: the all-orders sum for a presented configuration set is a finite discrete object whose exact evaluation yields one string on every machine; the optical limit's failure on halo nuclei is the field's own measured divergence, in the field's own journals; a court can replay presented configurations and grade approximation-versus-exact divergence against published cross sections in exact integers.

The frozen law (to be sealed at corpus stage)

Drafted here; frozen verbatim, with every integer bound to a named release string and accession, before the first configuration is scored.

  • S1 — Replication. D(12C, E) ∈ [30, 50] mb at each of E = 400, 550, 800 MeV/nucleon, the field's own printed band adopted as a frozen window. Integer comparison; three decisions; any miss is published.
  • S2 — Halo appointment. For each pinned halo row (accession named above): |q(σ_Full) − σ_EXFOR| ≤ 2 × DATA-ERR AND |q(σ_OLA) − σ_EXFOR| > 2 × DATA-ERR, all four quantities the integers of Crossing B and Crossing C (E1174013's window is ±120 mb, from its own printed ±60). For each control nuclide with a qualifying EXFOR row on 12C at its frozen scoring energy: |q(σ_Full) − σ_EXFOR| ≤ 2 × DATA-ERR. A named nuclide with no qualifying row prints ROW_ABSENT: that decision is VOID and published as VOID — never a silent drop, never counted as pass — and every S2 tally prints its denominator beside its markers, so absence and zero stay different answers. The exact reading must keep the archive's appointment where the smear misses it, and must not miss it anywhere a row exists.
  • S3 — Second-cumulant convergence. |q(σ_cumu2) − q(σ_Full)| ≤ 10 mb on every scored row, both quantities sealed by the cumu-2 and Full arms as defined in Crossing B — same lattice, same frozen weights, same degree-64 exponential rule. This grades the papers' "converges rapidly up to the second order" as an integer decision rather than a sentence.
  • S4 — The discrimination gate of Section zero, all four arms, with its already-frozen integers: always-green D = 0 exactly; replication band [30, 50] at three energies; margin M = 30 mb on three size-matched pairs at each pair's frozen halo-row energy; ceiling 60 mb breached by at most K = 2 of N = 8 controls at the frozen 800 MeV/nucleon, with the ⌊N/4⌋ adjustment rule of arm 4.
  • S5 — Byte identity. Every scored input matches its published fingerprint: AME2020 mass_1.mas20.txt at 472,648 bytes and NUBASE nubase_4.mas20.txt at 761,906 bytes as fetched 2026-08-26 (re-verified at corpus stage against the versioned static publication); every EXFOR anchor pinned with its archival date suffix (sub=E1174013:20260826 retrieval form) so a later archive correction is a new fact, never a silent move; the profile rail, the configuration sets, and the generator's full specification checksummed and published before scoring — the generator's seed integer is already frozen in this charter. A stranger with curl reproduces the corpus byte-exact or the seal does not stand.

What this protects

The matter radii of exotic nuclei — the numbers that made the halo famous — are not measured directly. They are extracted from interaction cross sections through Glauber-type analyses, which means every quoted femtometer inherits whichever level of the multiple-scattering expansion the analysis used. The field's own 2026 result puts an integer on what that inheritance can cost: 30–50 mb on the best-measured system in the chart, "considerably" on the halo case the theory exists to describe (VERIFIED above). The exotic-beam programs now running — FRIB, RIKEN RIBF, the facilities producing nuclides whose cross sections will land in EXFOR over the coming decade — will publish thousands of rows that pass through exactly this analysis chain.

What a replay court contributes is accounting integrity, and only that: a public, frozen, exact-integer record of what the approximation and the full calculation each print for the same presented configuration on the same public keys, graded against the same archived measurement, win and miss published alike. The archives themselves are treated as archives — accessions pinned at dated versions, byte counts recorded, cross-archive disagreements (the two half-life uncertainties, the phantom 1060 ± 10) stated on the page instead of averaged away. Nothing here consumes beam time, a target, or a detector; the entire study is a re-reading of what has already been measured and published, plus an exact replay anyone can run.

Honest limits

  • This court did not discover the shear. The optical limit's failure on halo nuclei is the field's own result, published by Horiuchi, Suzuki, and Wiringa in the field's own journals; the halo anomaly itself is Tanihata's, 1985. What Study 27 contributes is the grading discipline: law frozen before scoring, identity by exact accession, integers on public bytes, miss published beside win.
  • The sealed object is a frozen discrete pipeline, not the continuum integral. The impact-parameter lattice, the profile quantisation, the frozen rational π_rail, and the degree-64 exponential rule are choices, declared as Crossings A and B. Section zero's replication band is the check that these choices reproduce the field's printed numbers; if they do not, the page says VOID, not something softer.
  • Two rails are minted, not fetched. The profile rail and the configuration sets are produced by this program (deterministic generator, seed frozen in this charter, published checksums) because the papers' VMC configurations are not public files. They are the artifacts a stranger audits rather than re-downloads, and they are named here for that reason. A configuration set is never fabricated silently; an unsourceable one is CONFIG_ABSENT.
  • The court computes no quantum mechanics. No wave function, no amplitude, no potential fit, no energy dependence beyond the frozen table — the full list is its own section above. VMC and GFMC did the physics, on supercomputers; the court replays and grades.
  • The eikonal and adiabatic approximations are inherited, not tested. Both readings on this page live inside Glauber theory. A divergence between Glauber theory itself and experiment is outside this court's jurisdiction and would be reported as such.
  • Sourcing edges, stated. The two journal DOIs and publication dates are REPORTED via phys.org (APS pages 403-blocked automated fetch this session). The 6He overestimate has no printed number in the papers — "considerably" and figures only — and this charter derives no threshold from it; the 6He decision in S2 runs entirely on the EXFOR row's own printed error bar. The raw X4 of E1174013 itself states "No information on source of uncertainties" for its DATA-ERR (VERIFIED, 2026-08-26) — the ±60 is frozen as served, provenance and all. The Horiuchi PRL (2512.20095v2) prints its PLB 206, 592 reference with year 1985 against the standard 1988 — the companion PRC's reference list prints 1988 — both readings recorded, neither silently copied.
  • EXFOR moves; the anchors do not. The archive is refreshed continuously (same-day update stamp, VERIFIED 2026-08-26). Every anchor is pinned by archival date suffix, so the corpus is replayable against the exact bytes this charter saw even after upstream corrections — and an upstream correction, when one lands, is a new row on this page, not an edit to an old one.
  • No efficacy-shaped claim exists here to disclaim, and none is smuggled. This is a bookkeeping study on published scattering data. It recommends nothing to any facility, replaces no analysis pipeline, and grades only what it names.

Cross-links

Status: OPEN — charter published, corpus not yet ingested. Nothing here is sealed until the corpus runs.

⚡ Paradigm

✅ Sealed results

☀️🌑 Eclipse 2026

🌊 LIVE CLAIM

🌊 OPEN (no data)

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