Pith Number

pith:LNV6X2VX

pith:2025:LNV6X2VX55QLUPUT4NEL4Y6BAV

not attested not anchored not stored refs pending

Gram-like matrix preserving extensions and completions of noncommutative polynomials

Arijit Mukherjee, Arindam Sutradhar

arxiv:2501.12063 v2 · 2025-01-21 · math.OC · math.AC · math.AG · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LNV6X2VX55QLUPUT4NEL4Y6BAV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-07-05T11:28:13.557572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b6bebeab7ef60ba3e93e348be63c1056ff4dde3692888494b87b0c42829e2e7

Aliases

arxiv: 2501.12063 · arxiv_version: 2501.12063v2 · doi: 10.48550/arxiv.2501.12063 · pith_short_12: LNV6X2VX55QL · pith_short_16: LNV6X2VX55QLUPUT · pith_short_8: LNV6X2VX

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/LNV6X2VX55QLUPUT4NEL4Y6BAV \
  | 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: 5b6bebeab7ef60ba3e93e348be63c1056ff4dde3692888494b87b0c42829e2e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4caf26752dc78a1fad1be12023354dd0182679e387c5c459528394cf624ff327",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-01-21T11:35:24Z",
    "title_canon_sha256": "1a7743b64016c579236172d2806050dd78ffb2b6e9f8e0d54db906194a8c7967"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.12063",
    "kind": "arxiv",
    "version": 2
  }
}