FENn521 research chain

Chain 521 isolates the N and P-521 research lane.

FENn521 is the public research dossier for Chain 521, N, and the P-521 evidence path. It is deliberately written as a research-chain page: the primary concepts are signature shape, vector rejection behavior, circuit evidence, research contract modules, fixed N supply context, and the multisig release gate. The page avoids support-chain language so a technical reader can inspect N521 as its own cryptographic research lane.

The technical claim is precise: N521 makes the P-521 research surface visible as a public chain dossier with independent block progress and explicit release boundaries. That is the correct posture for advanced cryptographic work, because evidence can be inspectable before public release controls are opened.

That is why FENn521 stays separate from the FEN support economy. Its public job is to make research posture inspectable: readers can see the chain identity, the N asset boundary, the signature-shape record, the proof-case vocabulary, gas observations, contract roles, and multisig-gated release language without mistaking research evidence for unrestricted production authority.

Chain 521 public research-chain observation

Live N / P-521 evidence-lane continuity.

Chain 521 live progress is a public research-chain observation. It documents continuity for the N / P-521 evidence lane without becoming unrestricted release authority.

Live chain progress

Live Chain 521 progress

FENn521 keeps Chain 521 continuity visible while release authority remains gated. Last refresh: pending

Reading public block progress...

Public chain surface

Chain N521

Reading progress

Latest block

Reading

Sample move

Chain ID

521

Block progressreading

Public block read is pending; this card updates when the current block is returned.

Chain ID

521 / 0x209

Role

N / P-521 research chain

Function

signature-shape evidence, N521 research, circuit evidence, multisig-gated release posture

Boundary

research observation, not unrestricted release authority

Open FENn521 Explorer

Abstract 1. Section Abstract

Chain 521 is a cryptographic research dossier with a conservative release model.

This section documents N521 as a research artifact rather than a promotional token page. Its evidence surface includes vector behavior, signature shape, circuit proof cases, gas measurements, source-module roles, Chain 521 continuity, and the multisig release gate. The section is intentionally technical because every simplification would erase a verification boundary that matters to cryptographic reviewers.

Research theorem: public evidence can be dense and inspectable while release authority remains gated.

Definitions

Definition 1.132-byte signature: The public P-521 ECDSA signature form represented as r and s limbs of 66 bytes each.
Definition 2.Groth16 shape evidence: Circuit proof evidence about limb shape, range, modular arithmetic, and verifier behavior, scoped to the documented proof cases.
Definition 3.N: A fixed 10M Chain 521 research asset distinct from FEN and governed by published migration constraints involving burned FEN.
Definition 4.Multisig release gate: The condition that research contract release language remains conservative until full multisig implementation requirements are satisfied.

Research Questions

Research Question 1. RQ-521-01

What public evidence is sufficient for a P-521 research dossier?

The section requires vector behavior, 132-byte signature shape, circuit receipts, gas measurements, source roles, and release boundaries rather than unsupported claims of production cryptography.

Research Question 2. RQ-521-02

How is N separated from FEN?

N is documented as a fixed 10M Chain 521 research asset, while FEN remains the Chain 978 support asset and any future N mint is constrained by burned FEN migration rules.

Research Question 3. RQ-521-03

When can research evidence become release language?

Research evidence can be public before release, but public release language remains bounded by multisig implementation and any additional operational gates.

Formal Claim Register

Claim	Statement	Evidence	Boundary
Formal Claim 1. FC-521-01	Chain 521 is the N/P-521 research chain.	The section presents Chain 521 identity, live block progress, N asset context, P-521 signature shape, and research contract surfaces.	The section does not use Chain 521 as evidence for Chain 978 support-chain hosting claims.
Formal Claim 2. FC-521-02	The P-521 signature evidence has a precise public shape.	The page states 132 bytes as 66B r plus 66B s, with vector behavior and rejection cases listed.	Shape evidence is not equivalent to an unrestricted production verifier release.
Formal Claim 3. FC-521-03	Circuit and gas evidence are research artifacts.	Groth16 shape verifier cases, constraint counts, proof receipts, and gas measurements appear as evidence cards and receipt rows.	Research artifacts remain subject to multisig release and do not expose private signing or validator material.

Invariant Ledger

Invariant 1. INV-521-01

N is not FEN.

Definitions and boundary statements keep N as a 10M research asset and FEN as the support-chain protocol asset.

Invariant 2. INV-521-02

P-521 research remains release-gated.

Contract readiness, chain facts, and conclusion sections retain the multisig gate language.

Invariant 3. INV-521-03

Vector rejection cases are part of the evidence, not decorative detail.

The vector corpus records valid and adversarial cases including tamper, wrong message, wrong key, off-curve key, zero r, and zero s.

Invariant 4. INV-521-04

Gas measurements are bounded observations.

Gas rows are labeled by verifier shape and caveat rather than used as final production cost guarantees.

Evidence Matrix

Row	Artifact	Observation	Limitation
Evidence Row 1. 521-01	deployments/v59-p521-test-vectors.json	Records P-521 vector behavior across valid and rejected cases.	Vector behavior is research evidence, not a blanket proof of every deployed verification path.
Evidence Row 2. 521-02	deployments/v62-circom-circuit-report.json	Records Circom/Groth16 circuit readiness and proof-shape evidence.	Circuit readiness remains bounded by release-gate and verifier-specific assumptions.
Evidence Row 3. 521-03	deployments/v62-fenchain-n521-live-wallet-521.json	Records Chain 521 wallet evidence for the research-chain lane.	Wallet evidence does not expose private signing paths or remove the multisig release boundary.
Evidence Row 4. 521-04	docs/research/zk-p521-circuit-design.md	Documents the design context for P-521 circuit research.	Research documentation is not an external audit result unless paired with a scoped audit artifact.

chain 521 research flow

P-521 vectors, circuit shape, contract modules, and multisig release form one research map.

This diagram expresses FENn521 as an engineering dossier rather than a generic token page. Each node is a public research layer: vector behavior, signature shape, circuit receipts, contract surfaces, chain continuity, and the final release gate.

chain lane

521

Standalone N/P-521 research continuity surface.

signature form

66B + 66B

P-521 r and s limbs represented as a 132-byte signature.

asset cap

10M N

Fixed research asset context with future minting tied to burned FEN.

release mode

multisig

Public release remains gated by the full multisig implementation.

01 / vector corpusP-521The research lane begins with deterministic signature-vector behavior: valid signatures pass, while tampered signature, wrong message, wrong key, off-curve key, zero r, and zero s cases are rejected.

02 / signature shape132 bytesThe public evidence keeps the P-521 signature shape precise: r and s are each 66 bytes, and the uncompressed public key carries the expected 0x04 prefix form.

03 / circuit researchGroth16The circuit layer records limb shape, scalar-range assumptions, modular-addition behavior, proof generation, verifier estimates, and tamper rejection as research evidence.

04 / contract surfaceN521 modulesThe Solidity research path names the N asset profile, wallet shell, verifier shape, and registry concepts without exposing private release controls through the public interface.

05 / research chain521Chain 521 carries the public continuity signal for this research lane, giving the dossier its own live block progress and avoiding ambiguity with the FEN support chain.

06 / release gatemultisigThe release conclusion is deliberately conservative: evidence can be public, but the final contract-release posture waits for complete multisig implementation.

The chain 521 page is allowed to be deeply technical because its job is to document the evidence posture for N/P-521 research without blending that posture into the FEN support chain.

Research-chain identity

FENChain N521

Chain 521 is presented as the N/P-521 research chain with its own public identity, block progress, and release vocabulary.

Public chain ID

521 / 0x209

The chain identifier is part of the public evidence surface for the research lane and is kept separate from the FEN support-chain narrative.

Research asset

N

N is described as a fixed 10M research asset; future N minting requires burned FEN under published migration rules.

Signature evidence

132 bytes

The public research language preserves the P-521 ECDSA r+s signature shape, with each limb represented as 66 bytes.

Circuit posture

Groth16 shape

Circuit evidence is presented as a shape, range, and proof-receipt surface rather than a claim of unrestricted public contract release.

Release boundary

Multisig gate

The research contract path remains held for full multisig implementation before public release language can move beyond readiness evidence.

Chain 521 records

Published N521 account records stay scoped to the research chain.

The public record list is intentionally narrow: it shows the Chain 521 bootstrap account context that belongs to this dossier and avoids mixing in support-chain records from the FENchain page.

FENChain N521 / chain 521

N521 bootstrap prefund

Bootstrap account record

Public prefund account recorded in the standalone Chain 521 bootstrap receipt.

FENChain N521 / chain 521

N521 validator/minter

Validator/minter record

Public validator/minter role recorded for the Chain 521 research lane.

Contract status

Research contracts are described by role, not by uncontrolled release access.

The N521 contract language is deliberately specific: token profile, wallet shell, and registry evidence each have a different purpose, while public release remains tied to the multisig gate.

Chain-521 locked

FENRUAN521Token

N asset profile is described as a Chain 521 research asset with fixed supply context and published migration constraints.

Multisig release gate

FENchainN521Wallet

Owner-gated wallet research remains behind the multisig release boundary and is not exposed as a public execution control.

Audit-complete registry

FENchainN521BuildingBlockRegistry

Registry research organizes N521 module evidence and wallet attestations for the release-gated research path.

Four research surfaces, one release boundary.

The research work spans Solidity modules, vector behavior, circuit receipts, and public evidence records. The page uses technical language because each surface has a different verification purpose, and because flattening those surfaces would make the research lane harder for engineers to audit.

Solidity research

Contract research covers signature verification surfaces, P-521 shape checks, N521 wallet profile, registry evidence, and the N asset profile without presenting research code as an unrestricted production control.

signature verificationP-521 shape checksN profile

Vector research

The P-521 vector suite validates accepted signatures and rejection cases across malformed, mismatched, off-curve, and zero-limb inputs so the research language is tied to adversarial test behavior.

7 vector casestamper rejectionwrong-key rejection

Circom / Groth16

Circuit research records P-521 limb shape, scalar-range constraints, modular add/sub behavior, ECDSA-shaped scaffolding, Groth16 verifier shape, and proof receipts.

limb shapescalar rangeproof receipts

Evidence records

Public evidence records gas estimates, proof cases, caveats, and audit outcomes while keeping private release mechanics and operator credentials outside the UI.

gas evidenceproof casesaudit outcomes

Evidence matrix

Proven research signals and the exact boundary still held behind multisig.

P-521 vector suite

7 cases

@noble/curves secp521r1 validates good signatures and rejects wrong message, tampered signature, wrong key, off-curve key, zero r, and zero s.

Signature shape

132 bytes

ECDSA P-521 signature evidence is described as r + s, each 66 bytes, with public-key shape treated separately.

Research path

Audit complete

The P-521 / N521 contract research path is described as audit-complete while release remains held for the multisig implementation.

Groth16 shape verifier

6 cases

The ECDSA-shaped circuit compiles, generates proofs, accepts valid proof data, and rejects tampered public signals.

Circuit constraints

13,361

Constraint count remains visible as engineering traceability beside the release-gated contract path.

N521 wallet shell

Owner gated

Wallet records preserve the research boundary while public release waits for multisig control.

Public gas measurements, not hidden formulas.

Gas numbers are presented as receipt-backed engineering signals for the research lane. They help reviewers understand relative verification cost and proof-shape posture, but they do not expose protected formulas or bypass the multisig release gate.

P521Verifier shape guard

422,432 gas

Signature/public-key shape plus on-curve guard only.

Well-formed signature

57,948 gas

Helper measurement for 132-byte signature shape validation.

Groth16 P-521 shape

281,930 gas

Max gas estimate across six ECDSA-shaped proof cases.

Groth16 BigAdd

275,022 gas

Modular-addition proof verifier across six carry/reduction cases.

V61 mock lower bound

40,912 gas

Prototype lower bound only; not a Groth16 verifier and not P-521 arithmetic.

Research-chain conclusion.

FENn521 is best understood as a public cryptographic research chain with a conservative release model: the evidence is inspectable, the chain identity is explicit, the N supply context is constrained, and public contract release waits for the complete multisig gate.

Non-negotiable boundaries.

FENn521 is the N/P-521 research chain, not the FEN protocol support chain.

N is distinct from FEN: FEN is the protocol support asset, while N is the fixed 10M research asset for the Chain 521 dossier.

Future N minting requires burned FEN under published migration rules; that rule is a migration constraint, not a reason to merge the research lane into the support-chain page.

Research evidence can be public while multisig release controls, validator material, reserve mechanics, and private signing paths remain outside the UI.