Pith Number

pith:ZQWY53QD

pith:2006:ZQWY53QDANKJXLUFBZEEHKXGPF

not attested not anchored not stored refs pending

Linearity Defects of Face Rings

Kohji Yanagawa, Ryota Okazaki

arxiv:math/0607780 v3 · 2006-07-31 · 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{ZQWY53QDANKJXLUFBZEEHKXGPF}

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	2026-07-04T14:59:56.218850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc2d8eee0303549bae850e4843aae6795212a5ddeb7a811bb196e299a8e10dff

Aliases

arxiv: math/0607780 · arxiv_version: math/0607780v3 · doi: 10.48550/arxiv.math/0607780 · pith_short_12: ZQWY53QDANKJ · pith_short_16: ZQWY53QDANKJXLUF · pith_short_8: ZQWY53QD

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/ZQWY53QDANKJXLUFBZEEHKXGPF \
  | 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: cc2d8eee0303549bae850e4843aae6795212a5ddeb7a811bb196e299a8e10dff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a70fbbdffd9c38b6cb0eaf297b78ed672722254a5af9ae8b2003444873acd8e2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2006-07-31T06:23:36Z",
    "title_canon_sha256": "43c2bc9b7501506d7928db255de22e0cdc14305def7e81ce8ae4a992b302b9ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607780",
    "kind": "arxiv",
    "version": 3
  }
}