Pith Number

pith:QC27US27

pith:2019:QC27US27PXDADAGRY72QJKMNHO

not attested not anchored not stored refs pending

Three-Manifold Quantum Invariants and Mock Theta Functions

Francesca Ferrari, Gabriele Sgroi, Miranda C. N. Cheng

arxiv:1912.07997 v3 · 2019-12-17 · math.NT · hep-th · math-ph · math.GT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QC27US27PXDADAGRY72QJKMNHO}

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

Quantum invariants of 3-manifolds and links: a review

Receipt and verification

First computed	2026-07-05T00:48:01.737251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80b5fa4b5f7dc60180d1c7f504a98d3b80cd5ec7bea855611ff3f12c4abaf4b2

Aliases

arxiv: 1912.07997 · arxiv_version: 1912.07997v3 · doi: 10.48550/arxiv.1912.07997 · pith_short_12: QC27US27PXDA · pith_short_16: QC27US27PXDADAGR · pith_short_8: QC27US27

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/QC27US27PXDADAGRY72QJKMNHO \
  | 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: 80b5fa4b5f7dc60180d1c7f504a98d3b80cd5ec7bea855611ff3f12c4abaf4b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ecf175ef33acd3f971b39db5d7bbe3f2b4ccec65d8a1bce3ba41d82319d5b85",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.GT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-12-17T13:25:01Z",
    "title_canon_sha256": "8476026106ca373649d73a27a8ee4025dd7563e41c977eaf2089e6f945669df0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.07997",
    "kind": "arxiv",
    "version": 3
  }
}