Pith Number

pith:J7RQN64A

pith:2015:J7RQN64A23WRERRQSE7W3U6QW5

not attested not anchored not stored refs pending

Integral positive (negative) quandle cocycle invariants are trivial for knots

Hongzhu Gao, Zhiyun Cheng

arxiv:1502.03904 v1 · 2015-02-13 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J7RQN64A23WRERRQSE7W3U6QW5}

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	2026-05-18T01:22:41.199780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fe306fb80d6ed124630913f6dd3d0b763890605b691148e12fe3ba7255541ac

Aliases

arxiv: 1502.03904 · arxiv_version: 1502.03904v1 · doi: 10.48550/arxiv.1502.03904 · pith_short_12: J7RQN64A23WR · pith_short_16: J7RQN64A23WRERRQ · pith_short_8: J7RQN64A

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/J7RQN64A23WRERRQSE7W3U6QW5 \
  | 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: 4fe306fb80d6ed124630913f6dd3d0b763890605b691148e12fe3ba7255541ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "531ea5471c0e0f9055d2ea27f7a46a90233f56bd296aeffda958ef92b1487971",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-02-13T07:23:52Z",
    "title_canon_sha256": "b7f239c0a236ad70b076fbbb55e0f247de2b01e26bda494878194a0be76f8099"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.03904",
    "kind": "arxiv",
    "version": 1
  }
}