Affine Earth Lattice Endpoints

Explore the lattice courts — live on affine.earth

Researchers replay the sealed studies on the same membrane travelers already use. No new host. No canvas. Integers only.

Start in the main UI (look only): https://affine.earth/language-game/#researcher

That view is the client experience. It teaches what Affine.Earth is and how UUM-8D entities (vQbit, M⁸ = S⁴ × C⁴, TauAnchor, Jordan bond, GOP frame, lattice court) play in the digital twin. It GETs the public catalog. It sends no location, no wallet, no name, no source. Court POSTs stay on this page as an explicit second act.

Live 2026-08-23. Nine cells serve one ELF (984e5f57364b70ad…). Catalog: lattice_courts.domain_count = 9, role_count = 28. Apex GET /language-invariant/games → HTTP 200.

Hologram WASM is a different face. These courts do not go through it. The researcher look path is a panel on the same /language-game/ page travelers already use.

Public wiki of the same studies: uum8dSolarResearch. DFT map: Fourier Phantom — Anima FNO is their claim; Affine LIVE courts are 11 / 12 / 13.

Agent bind — the court is already MCP

Public client tree: clients/math-court-mcp. Wrappers POST to the remote. They compute no court.

{
  "mcpServers": {
    "affine-earth-math-court": {
      "url": "https://affine.earth/language-invariant/mcp"
    }
  }
}

SSE face: https://affine.earth/language-invariant/mcp/sse

tools/list on that URL returns the fifteen tools the cell serves (execute_transition, verify_jordan_bond, twin.robotics.evaluate_exact_ik, …). A float POST is HTTP 400 REFUSED_FLOAT. Geometry dilation: 12 seals count 169 against float adversary 216.

Registry: earth.affine/math-court · descriptor clients/math-court-mcp/server.json. Prove: bash clients/math-court-mcp/prove/prove-math-court-agent-ingest.sh. The Swift membrane is not in this repository.

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0. Open the catalog (start here)

curl -sS https://affine.earth/language-invariant/games

Read lattice_courts:

Field	What it is
domains[].id	Court name — also the {domain} path segment
domains[].roles[].role	Who may POST
domains[].roles[].may_ingest	Integer keys the court will read
domains[].roles[].http.POST	Ingest URL
domains[].roles[].http.GET	Context URL
entropy_delta / qfot_cost	ΔD_H on entropy_delta_dh_structural
flourishing_root	Why the court exists for people

Same catalog as a study list:

curl -sS https://affine.earth/language-invariant/np-hard

One domain’s contract + the formal-manifold agent:

curl -sS https://affine.earth/language-invariant/game/geometry/context

---

1. The door

POST /language-invariant/game/{domain}/ingest

Field	Required	Law
source	yes	Empty → REFUSED_UNATTRIBUTED (400)
role	yes	Unknown → REFUSED_UNKNOWN_ROLE (404)
one may_ingest key	yes	None → REFUSED_EMPTY_PAYLOAD (400)
numbers	integers	1.5 / 1e3 / IEEE → REFUSED_FLOAT (400)
wallet_hash	no	If present, same QFOT debit as POST /language-invariant/domain-debit

Keys may sit at the top level or under payload. The cell takes payload when it is an object, otherwise the body.

GET is context. POST is the court. Onboard is POST only (GET /language-invariant/economics-onboard is 404).

---

2. Every role (28)

Domain	ΔD_H	Roles	Ingest keys	Study / wiki
geometry	1/5	cad_engineer · digital_twin · regulator	polytope_id dilation vertices	Study 11
chance	1/4	quantum_info · compiler · consensus	rounds	Study 12
algebra	1/5	phenomenologist · qft_theorist	word presentation	Study 13
physics	1/3	experimentalist · detector · theorist	clock track table_counts	Impact
qcd	1/3	jet_analyst · phenomenologist	q_bin jet_counts color_isolated dilation_t	QCD
health	1/2	clinician · pharmacist · trialist · regulator	mass_milli vol_milli tau_s arm_counts	Impact
finance	1/2	trader · risk · clearing · auditor	lots ticks loss_ticks threshold_ticks	Impact
cs	1/5	compiler · consensus · ml_engineer	num den payload_sha256d label_int	Impact
fluids	1/3	designer · cfd_vendor · certifier · operator	phi_in phi_out residual_int	Impact
dynamo	—	researcher · theorist · steward	q r n d	Study 21 · kill shot

Polytopes the geometry court already grades: unit_square unit_triangle simplex3 hle_poly_d2 hle_poly_d3.

Algebra words the corpus already grades: Z2_a2b Z2_aba Z2_abAB Z2_ba S3_abab. A lone letter e is not a word and is not a float token the court will run.

---

3. Replay the sealed studies (copy-paste)

Measured on https://affine.earth 2026-08-23 after the nine-cell roll. Each POST returned HTTP 200 and lattice_court.status = CALORIE.

# Study 11 — Ehrhart. unit_square @ t=12 → count 169, vol 1/1, float adversary 216
curl -sS -X POST https://affine.earth/language-invariant/game/geometry/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"cad_engineer","polytope_id":"unit_square","dilation":12}'

# Study 12 — parallel repetition. n=1 → discrete (3/4)^1
curl -sS -X POST https://affine.earth/language-invariant/game/chance/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"quantum_info","rounds":1}'

# Study 13 — Eisenstein linking. word Z2_aba
curl -sS -X POST https://affine.earth/language-invariant/game/algebra/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"phenomenologist","word":"Z2_aba"}'

Measured lattice_court (geometry, 2026-08-23):

{
  "status": "CALORIE",
  "verdict": "WIN",
  "domain": "geometry",
  "role": "cad_engineer",
  "polytope_id": "unit_square",
  "dilation": 12,
  "lattice_count": 169,
  "volume": "1/1",
  "float_adversary": 216,
  "adversary_miss": true,
  "proven_marker": "STUDY11_EHRHART_VOLUME_PROVEN"
}

That is the same row as Study 11 Results: count 169, float 216, adversary MISS, primary WIN.

Same court through the existing formal-manifold id:

curl -sS -X POST https://affine.earth/language-invariant/game/formal_manifold/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","domain":"geometry","role":"cad_engineer","polytope_id":"unit_square","dilation":12}'

---

4. The other six courts

Measured 2026-08-23, all HTTP 200, lattice_court CALORIE.

# physics — table is the court (CONTRACT)
curl -sS -X POST https://affine.earth/language-invariant/game/physics/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"experimentalist","clock":1,"track":1}'

# qcd — freedom is dilation
curl -sS -X POST https://affine.earth/language-invariant/game/qcd/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"phenomenologist","q_bin":1,"dilation_t":2}'

# health — C = n/d
curl -sS -X POST https://affine.earth/language-invariant/game/health/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"pharmacist","mass_milli":250,"vol_milli":100}'

# finance — PnL = lots × ticks  → 21
curl -sS -X POST https://affine.earth/language-invariant/game/finance/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"trader","lots":3,"ticks":7}'

# cs — associative rationals
curl -sS -X POST https://affine.earth/language-invariant/game/cs/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"compiler","num":3,"den":5}'

# fluids — sum Φ = 0
curl -sS -X POST https://affine.earth/language-invariant/game/fluids/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"designer","phi_in":4,"phi_out":4}'

Domain	Role used	Measured verdict
physics	experimentalist	CONTRACT
qcd	phenomenologist	WIN
health	pharmacist	WIN · concentration 250/100
finance	trader	WIN · pnl_ticks 21
cs	compiler	WIN
fluids	designer	WIN

---

5. Reproduce the refusals

Measured 2026-08-23, all HTTP 400.

# IEEE payload
curl -sS -X POST https://affine.earth/language-invariant/game/geometry/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"cad_engineer","dilation":1.5}'
# → status REFUSED_FLOAT

# no may_ingest key
curl -sS -X POST https://affine.earth/language-invariant/game/geometry/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"cad_engineer"}'
# → status REFUSED_EMPTY_PAYLOAD

# no source
curl -sS -X POST https://affine.earth/language-invariant/game/geometry/ingest \
  -H 'content-type: application/json' \
  -d '{"role":"cad_engineer","polytope_id":"unit_square","dilation":12}'
# → status REFUSED_UNATTRIBUTED

A float never reaches the ledger. A MISS (adversary agreed, residual ≠ 0, isolated color) still ran the law.

---

6. Onboard and price

Consent + a mainnet receive address. The cell hashes the address. It refuses private_key / mnemonic / wif.

curl -sS -X POST https://affine.earth/language-invariant/economics-onboard \
  -H 'content-type: application/json' \
  -d '{"address":"bc1q…","consent_create_wallet":true}'

Receipt fields: qfot_account_id, genesis_qfot (100/1), btc_address_hash_sha256. That hash is wallet_hash on later ingest.

curl -sS https://affine.earth/language-invariant/economics-config

domain_cost_table lists geometry…fluids. base_qfot is entropy_delta (bare − resolved). Axis: entropy_delta_dh_structural. Never token count.

Optional debit on the same ingest:

curl -sS -X POST https://affine.earth/language-invariant/game/geometry/ingest \
  -H 'content-type: application/json' \
  -d '{"source":"researcher","role":"cad_engineer","wallet_hash":"<sha256>","polytope_id":"unit_square","dilation":12}'

When wallet_hash is present the receipt grows a qfot object (DEBITED or REFUSED_INSUFFICIENT_QFOT).

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7. How to read the receipt

The HTTP body is the existing game ingest (CALORIE_GAME_INGEST, statement_digest, guide). The court is the nested object:

lattice_court.verdict     WIN | MISS | CONTRACT
lattice_court.volume      "num/den"     (geometry)
lattice_court.lattice_count
lattice_court.float_adversary
lattice_court.proven_marker
lattice_court.wiki        this wiki, per study

LAW 1: the win is the verified bond, not custody of coins. Genesis QFOT is a routing credit, not a claim on BTC.

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8. Pin one cell (optional)

Apex affine.earth is the nine-cell set. To name a cell:

curl -sS --resolve affine.earth:443:135.181.88.134 \
  https://affine.earth/language-invariant/games

HEL: 77.42.85.60 135.181.88.134 77.42.32.156 77.42.88.110 37.27.7.9
NBG: 37.120.187.247 152.53.91.220 152.53.88.141 37.120.187.174

Every cell listed answered the same binary sha on 2026-08-23.

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Reading: Impact study · QCD · The lattice holds · Sovereign onboard