Pith Number

pith:T47X4UDE

pith:2026:T47X4UDER5UTX3RLQSC2GZRA3P

not attested not anchored not stored refs pending

Zero-Error Recovery under Deterministic Partial Views: Matroid Bounds and Verifiable Realizability

Tristan Simas

For affine realized state families, restricted coordinate ranks form a representable matroid that certifies polynomial-time upper bounds on zero-error confusability and asymptotic capacity.

arxiv:2602.23520 v9 · 2026-02-26 · cs.IT · cs.PL · math.IT

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\pithnumber{T47X4UDER5UTX3RLQSC2GZRA3P}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one-shot confusability and asymptotic capacity, with rank additivity matching direct-sum block composition.

C2weakest assumption

The latent state family must be affine realized with explicit linear presentations for the matroid certificate and rank-additivity claims to apply; the abstract does not state how restrictive this class is.

C3one line summary

Zero-error recovery under partial views reduces to graph T-colorability and Shannon capacity, with representable matroid certificates providing bounds for affine families and Lean-verified conditions for host realizability.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-21T01:04:23.787556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f3f7e50648f693bee2b8485a36620dbdb04bdcea8fbb7abe35a2636bcd6d145

Aliases

arxiv: 2602.23520 · arxiv_version: 2602.23520v9 · doi: 10.48550/arxiv.2602.23520 · pith_short_12: T47X4UDER5UT · pith_short_16: T47X4UDER5UTX3RL · pith_short_8: T47X4UDE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T47X4UDER5UTX3RLQSC2GZRA3P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9f3f7e50648f693bee2b8485a36620dbdb04bdcea8fbb7abe35a2636bcd6d145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89c86ca9b7a938da70b5ca7944ce1f33f4e9246e0fd9f0924fb917f10c77501d",
    "cross_cats_sorted": [
      "cs.PL",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-02-26T21:47:11Z",
    "title_canon_sha256": "6518c37e04b17766e90456ca5060f9a3575c2f26ca7a29e03e2c48a4c172b8ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.23520",
    "kind": "arxiv",
    "version": 9
  }
}