Pith Number

pith:VGI2CLLJ

pith:2011:VGI2CLLJEG4VWWEQFJ7S6ES6FQ

not attested not anchored not stored refs pending

A dual to tight closure theory

Karl Schwede, Neil Epstein

arxiv:1110.4647 v3 · 2011-10-20 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGI2CLLJEG4VWWEQFJ7S6ES6FQ}

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	2026-05-18T02:29:25.541097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a991a12d6921b95b58902a7f2f125e2c00c3d5dbc4e63871b0d470b55713a7e8

Aliases

arxiv: 1110.4647 · arxiv_version: 1110.4647v3 · doi: 10.48550/arxiv.1110.4647 · pith_short_12: VGI2CLLJEG4V · pith_short_16: VGI2CLLJEG4VWWEQ · pith_short_8: VGI2CLLJ

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/VGI2CLLJEG4VWWEQFJ7S6ES6FQ \
  | 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: a991a12d6921b95b58902a7f2f125e2c00c3d5dbc4e63871b0d470b55713a7e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0c13ae7981c1b1b2337ffe7071ef6a36e80348aff677f3dc53806831eb45f62",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-10-20T20:48:56Z",
    "title_canon_sha256": "a6252d2d42f246c60549d3c75d177a1600ae416772ef2c03e8f6a4fef2dfdbad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4647",
    "kind": "arxiv",
    "version": 3
  }
}