Pith Number

pith:VTAFFA63

pith:2011:VTAFFA63MN6SQKC54MI2FU5SC2

not attested not anchored not stored refs pending

Betti Numbers of Syzygies and Cohomology of Coherent Sheaves

David Eisenbud, Frank-Olaf Schreyer

arxiv:1102.3559 v1 · 2011-02-17 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTAFFA63MN6SQKC54MI2FU5SC2}

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	2026-05-18T04:28:28.849994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acc05283db637d28285de311a2d3b216965b1f06ac4db28c5dab0f0b8695c8ee

Aliases

arxiv: 1102.3559 · arxiv_version: 1102.3559v1 · doi: 10.48550/arxiv.1102.3559 · pith_short_12: VTAFFA63MN6S · pith_short_16: VTAFFA63MN6SQKC5 · pith_short_8: VTAFFA63

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/VTAFFA63MN6SQKC54MI2FU5SC2 \
  | 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: acc05283db637d28285de311a2d3b216965b1f06ac4db28c5dab0f0b8695c8ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "206a51a8e8e2ceb26fe4be1039cf81dbe17cdf99af3a9f238ac80a3d18a24669",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-02-17T11:13:41Z",
    "title_canon_sha256": "6587b32efff89f25583aea9654c67408dcc59f9e0ff59bc938cdae8c8020b07e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3559",
    "kind": "arxiv",
    "version": 1
  }
}