Pith Number

pith:Z4KYUZU3

pith:2011:Z4KYUZU37NJI7IGC52APXTSNQF

not attested not anchored not stored refs pending

Criteria for flatness and injectivity

Neil Epstein, Yongwei Yao

arxiv:1103.4726 v1 · 2011-03-24 · 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{Z4KYUZU37NJI7IGC52APXTSNQF}

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	2026-05-18T01:24:38.923433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf158a669bfb528fa0c2ee80fbce4d8174a3bd323382b0bfc5498c2a2246cee2

Aliases

arxiv: 1103.4726 · arxiv_version: 1103.4726v1 · doi: 10.48550/arxiv.1103.4726 · pith_short_12: Z4KYUZU37NJI · pith_short_16: Z4KYUZU37NJI7IGC · pith_short_8: Z4KYUZU3

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/Z4KYUZU37NJI7IGC52APXTSNQF \
  | 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: cf158a669bfb528fa0c2ee80fbce4d8174a3bd323382b0bfc5498c2a2246cee2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a2aba41b9a40612d807a2d72fa50d4e2753f27d33f87fcc67cbc5519a4522b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-03-24T10:42:54Z",
    "title_canon_sha256": "3d20ed1f01688ce998a33bee351ba06e2e0ed3a18feb39a881beaf466133dea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4726",
    "kind": "arxiv",
    "version": 1
  }
}