Pith Number

pith:KDP2RGOX

pith:2014:KDP2RGOXMMLZX7KHCHZFBWAQYT

not attested not anchored not stored refs pending

Gotzmann's persistence theorem for finite modules

Gustav S{\ae}d\'en St{\aa}hl

arxiv:1411.7940 v2 · 2014-11-28 · 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{KDP2RGOXMMLZX7KHCHZFBWAQYT}

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	2026-05-18T00:31:22.923624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50dfa899d763179bfd4711f250d810c4dbfef9da5e5ff769be3761f83d482038

Aliases

arxiv: 1411.7940 · arxiv_version: 1411.7940v2 · doi: 10.48550/arxiv.1411.7940 · pith_short_12: KDP2RGOXMMLZ · pith_short_16: KDP2RGOXMMLZX7KH · pith_short_8: KDP2RGOX

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/KDP2RGOXMMLZX7KHCHZFBWAQYT \
  | 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: 50dfa899d763179bfd4711f250d810c4dbfef9da5e5ff769be3761f83d482038

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca72b412d5e531a1ee043eceb824f39a1da95b3b34f14e6c5172ec05261d209f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-11-28T16:50:21Z",
    "title_canon_sha256": "a089bdbe637dfd57f8f9b3418dd894d4b39cfb63b37a211b10c4e1ada9f9828a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.7940",
    "kind": "arxiv",
    "version": 2
  }
}