Pith Number

pith:ASXTXPRI

pith:2025:ASXTXPRIXXTL7JSFHP3QBY5Y2D

not attested not anchored not stored refs pending

A basis theorem for Genus-One Conformal Blocks and modular invariance of intertwining operators

Jianqi Liu, Xu Gao

arxiv:2508.01294 v2 · 2025-08-02 · math.QA · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ASXTXPRIXXTL7JSFHP3QBY5Y2D}

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	2026-06-26T00:15:22.315476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04af3bbe28bde6bfa6453bf700e3b8d0ca1750a5b8d3170a4c243c07df57dea1

Aliases

arxiv: 2508.01294 · arxiv_version: 2508.01294v2 · doi: 10.48550/arxiv.2508.01294 · pith_short_12: ASXTXPRIXXTL · pith_short_16: ASXTXPRIXXTL7JSF · pith_short_8: ASXTXPRI

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/ASXTXPRIXXTL7JSFHP3QBY5Y2D \
  | 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: 04af3bbe28bde6bfa6453bf700e3b8d0ca1750a5b8d3170a4c243c07df57dea1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8a6aecfd678cf50d9da7d723298afa2dd2248828b088912670bba28586b5606",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2025-08-02T10:03:39Z",
    "title_canon_sha256": "7d7af0f7fe8feefb610ddcccaf44f57c12ed32fdc282b7bc47ee47990b1c8c2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.01294",
    "kind": "arxiv",
    "version": 2
  }
}