Pith Number

pith:HL4WU5QA

pith:2016:HL4WU5QASM5T4JTPVQFBG3OSHF

not attested not anchored not stored refs pending

Harmonic volume and its applications

Yuuki Tadokoro

arxiv:1602.02267 v1 · 2016-02-06 · math.GT · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HL4WU5QASM5T4JTPVQFBG3OSHF}

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.

Cited by

1 paper in Pith

Ceresa Cycles of $X_{0}(N)$

Receipt and verification

First computed	2026-05-18T01:21:10.460100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af96a7600933b3e266fac0a136dd23941ee0167e46d971c60ada12e6188616b

Aliases

arxiv: 1602.02267 · arxiv_version: 1602.02267v1 · doi: 10.48550/arxiv.1602.02267 · pith_short_12: HL4WU5QASM5T · pith_short_16: HL4WU5QASM5T4JTP · pith_short_8: HL4WU5QA

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/HL4WU5QASM5T4JTPVQFBG3OSHF \
  | 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: 3af96a7600933b3e266fac0a136dd23941ee0167e46d971c60ada12e6188616b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0898428a79f569d06a9cb7b7c5620e76e59cb02ce9fa6bd1997abb1f412340ce",
    "cross_cats_sorted": [
      "math.AG",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-02-06T15:44:20Z",
    "title_canon_sha256": "a44099d4359aec692013b4b0a6485668f2859d5214e45ec1a68e8b7f39491fd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.02267",
    "kind": "arxiv",
    "version": 1
  }
}