Pith Number

pith:27MHOTRK

pith:2019:27MHOTRKFTMPTYT3AUL4Q4ZP6J

not attested not anchored not stored refs pending

Modules over posets: commutative and homological algebra

Ezra Miller

arxiv:1908.09750 v2 · 2019-08-26 · math.AC · math.AG · math.AT · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27MHOTRKFTMPTYT3AUL4Q4ZP6J}

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	2026-07-05T01:26:38.781176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7d8774e2a2cd8f9e27b0517c8732ff25809c2e6e5a4b2d3d8453414e26a5b1b

Aliases

arxiv: 1908.09750 · arxiv_version: 1908.09750v2 · doi: 10.48550/arxiv.1908.09750 · pith_short_12: 27MHOTRKFTMP · pith_short_16: 27MHOTRKFTMPTYT3 · pith_short_8: 27MHOTRK

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/27MHOTRKFTMPTYT3AUL4Q4ZP6J \
  | 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: d7d8774e2a2cd8f9e27b0517c8732ff25809c2e6e5a4b2d3d8453414e26a5b1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89630bb67b4d9468b8bd53174363d172a1f5bb98af3d597b56bbb466fb162346",
    "cross_cats_sorted": [
      "math.AG",
      "math.AT",
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-08-26T15:45:42Z",
    "title_canon_sha256": "c2ff681713a1927dd4c5d536bb4ed95ef7e88b83470ef947c1f20e9deb3d5553"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09750",
    "kind": "arxiv",
    "version": 2
  }
}