Pith Number

pith:V7B4DB42

pith:2013:V7B4DB42644KXVWM3TC6M2J54V

not attested not anchored not stored refs pending

Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves

Albert Schwarz, Jia-Ming Liou, Renjun Xu

arxiv:1308.6374 v4 · 2013-08-29 · math.AG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7B4DB42644KXVWM3TC6M2J54V}

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	2026-05-18T02:25:26.726018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188

Aliases

arxiv: 1308.6374 · arxiv_version: 1308.6374v4 · doi: 10.48550/arxiv.1308.6374 · pith_short_12: V7B4DB42644K · pith_short_16: V7B4DB42644KXVWM · pith_short_8: V7B4DB42

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/V7B4DB42644KXVWM3TC6M2J54V \
  | 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: afc3c1879af738abd6ccdcc5e6693de55c2deeddb686c590d7553278e90e7188

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ebbdc2a5827e14c1d4e5d6595245a23a123eb4c1a3049fd73581ce2f9eadf83",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-08-29T06:31:43Z",
    "title_canon_sha256": "8c4726cd53510a8a327a4cc13b2acca6e6e3c7937a216068a0470df37acdfd53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6374",
    "kind": "arxiv",
    "version": 4
  }
}