CAPSULA
Rank-Indexed Procedural Reconstruction and Constrained Combinatorial Proof-of-Work
CAPSULA is a research project that explores how information and computational work can be represented as procedural discovery rather than explicit binary storage or brute-force hash computation.
Instead of storing data directly, CAPSULA models results as coordinates (ranks) inside constrained combinatorial spaces, recoverable only through deterministic execution.
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What CAPSULA Is
CAPSULA is composed of two independent and orthogonal modules.
Procedural Reconstruction (Deterministic)
This module provides a reversible and deterministic process where binary data is reconstructed from compact parameters and a rank value.
The reconstruction follows the model:
parameters + rank → procedural execution → binary output
The binary data is never stored explicitly. It only exists after executing the reconstruction algorithm.
Key properties: • Deterministic • Reversible • Linear-time reconstruction • Fully context-dependent
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Constrained Combinatorial Proof-of-Work (Probabilistic)
This module defines a Proof-of-Work mechanism based on discovering rare decision paths inside constrained combinatorial trees.
The work consists of finding a decision path (CP) such that its rank, under a given parameter set, is lower than a target threshold.
Instead of searching for hash collisions, miners explore structured decision spaces governed by mathematical constraints.
Key properties: • Probabilistic • Asymmetric (expensive to find, cheap to verify) • Parameter-dependent • Independent of cryptographic hash difficulty
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What CAPSULA Is Not
To avoid misinterpretation, CAPSULA is not: • A data compression algorithm • A file storage system • A cryptographic primitive • A production cryptocurrency • A replacement for SHA-256, ECDSA, or IPFS
CAPSULA is a research and educational system focused on computation, structure, and procedural reconstruction.
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Architectural Separation (Critical)
The two modules are mathematically independent and must not be conflated.
Procedural Reconstruction: parameters + rank → binary Deterministic and reversible
Proof-of-Work: parameters → discover rare decision paths Probabilistic and irreversible
They may coexist in the same ecosystem, but they serve different purposes and must remain conceptually separate to preserve correctness and academic validity.
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Project Status
Current state of the project: • Formal architecture defined • Rank function mathematically specified • Deterministic unranking and reconstruction validated • Small-scale Proof-of-Work experiments completed • Network protocols under research • Economic and incentive layers intentionally out of scope
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Documentation
The full technical specification is available in the whitepaper:
WHITEPAPER.md
The whitepaper includes formal definitions, rank mathematics, pseudocode, complexity analysis, security considerations, and experimental validation.
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Research Focus
CAPSULA investigates: • Computation-for-results tradeoffs • Rank-indexed procedural data • Constrained combinatorial search • Non-hash-based Proof-of-Work models • Deterministic reconstruction from compact representations
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Intended Use
CAPSULA is intended for:Perfeito, entendi agora 👍 Você quer o README inteiro em texto corrido, sem bloco de código, sem ```, do jeito que o GitHub espera quando você cola direto no editor.
Aqui está o README.md COMPLETO, em inglês, em um único texto contínuo, pronto para copiar e colar direto:
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CAPSULA
Rank-Indexed Procedural Reconstruction and Constrained Combinatorial Proof-of-Work
CAPSULA is a research project that explores how information and computational work can be represented as procedural discovery rather than explicit binary storage or brute-force hash computation.
Instead of storing data directly, CAPSULA models results as coordinates (ranks) inside constrained combinatorial spaces, recoverable only through deterministic execution.
⸻
What CAPSULA Is
CAPSULA is composed of two independent and orthogonal modules.
Procedural Reconstruction (Deterministic)
This module provides a reversible and deterministic process where binary data is reconstructed from compact parameters and a rank value.
The reconstruction follows the model:
parameters + rank → procedural execution → binary output
The binary data is never stored explicitly. It only exists after executing the reconstruction algorithm.
Key properties: • Deterministic • Reversible • Linear-time reconstruction • Fully context-dependent
⸻
Constrained Combinatorial Proof-of-Work (Probabilistic)
This module defines a Proof-of-Work mechanism based on discovering rare decision paths inside constrained combinatorial trees.
The work consists of finding a decision path (CP) such that its rank, under a given parameter set, is lower than a target threshold.
Instead of searching for hash collisions, miners explore structured decision spaces governed by mathematical constraints.
Key properties: • Probabilistic • Asymmetric (expensive to find, cheap to verify) • Parameter-dependent • Independent of cryptographic hash difficulty
⸻
What CAPSULA Is Not
To avoid misinterpretation, CAPSULA is not: • A data compression algorithm • A file storage system • A cryptographic primitive • A production cryptocurrency • A replacement for SHA-256, ECDSA, or IPFS
CAPSULA is a research and educational system focused on computation, structure, and procedural reconstruction.
⸻
Architectural Separation (Critical)
The two modules are mathematically independent and must not be conflated.
Procedural Reconstruction: parameters + rank → binary Deterministic and reversible
Proof-of-Work: parameters → discover rare decision paths Probabilistic and irreversible
They may coexist in the same ecosystem, but they serve different purposes and must remain conceptually separate to preserve correctness and academic validity.
⸻
Project Status
Current state of the project: • Formal architecture defined • Rank function mathematically specified • Deterministic unranking and reconstruction validated • Small-scale Proof-of-Work experiments completed • Network protocols under research • Economic and incentive layers intentionally out of scope
⸻
Documentation
The full technical specification is available in the whitepaper:
WHITEPAPER.md
The whitepaper includes formal definitions, rank mathematics, pseudocode, complexity analysis, security considerations, and experimental validation.
⸻
Research Focus
CAPSULA investigates: • Computation-for-results tradeoffs • Rank-indexed procedural data • Constrained combinatorial search • Non-hash-based Proof-of-Work models • Deterministic reconstruction from compact representations
⸻
Intended Use
CAPSULA is intended for: • Academic research • Educational demonstrations of Proof-of-Work • Experimental distributed computation markets • Exploration of procedural data systems
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License
MIT License
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CAPSULA is composed of two independent but interoperable mechanisms: a combinatorial Proof-of-Work module and a deterministic procedural reconstruction module. Together, they demonstrate how computational rarity (mining) can be cleanly separated from deterministic reconstruction (unranking), without mixing concerns.
The first step is mining. Mining in CAPSULA does not recover data and does not reconstruct binary content. Its sole purpose is to discover a rare rank that satisfies a constrained combinatorial rule set. To run the mining demo, execute:
python demo_mining.py
A typical output looks like this:
⛏️ MINING (target rank < 3)...
✅ BLOCK MINED in 8 attempts
CP: [0, 0, 1]
Rank: 1
Hashrate: ~31k CPs/s
Valid: True
This output shows that the miner probabilistically discovered a valid checkpoint path whose rank is below the target threshold. The discovered rank is the only value that matters for the next step.
The second step is deterministic reconstruction. Given a rank, CAPSULA can reconstruct the exact checkpoint path without any search, randomness, or mining. This process runs in linear time and is fully deterministic. To demonstrate this, run:
python demo_unrank.py
Using the rank obtained during mining, the output will be:
Input rank: 1
Reconstructed CP: [0, 0, 1]
This confirms that the rank uniquely identifies a valid path and that the checkpoint is simply a deterministic expansion of that rank under the same parameters.
The key takeaway is that mining and reconstruction are mathematically independent. Mining discovers rarity through computation, while unranking reconstructs structure through deterministic rules. CAPSULA intentionally separates these mechanisms to preserve conceptual clarity, correctness, and academic integrity.hrate: ~31k CPs/s Valid: True