Pith Number

pith:2KFG7OX2

pith:2018:2KFG7OX2MQKQNM2FHF25PU7DO5

not attested not anchored not stored refs pending

Quantum modular forms and plumbing graphs of 3-manifolds

Antun Milas, Karl Mahlburg, Kathrin Bringmann

arxiv:1810.05612 v2 · 2018-10-12 · math.QA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2KFG7OX2MQKQNM2FHF25PU7DO5}

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	2026-05-17T23:42:15.366442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d28a6fbafa641506b3453975d7d3e37772a58bfc071683d6d4afba686b8972c6

Aliases

arxiv: 1810.05612 · arxiv_version: 1810.05612v2 · doi: 10.48550/arxiv.1810.05612 · pith_short_12: 2KFG7OX2MQKQ · pith_short_16: 2KFG7OX2MQKQNM2F · pith_short_8: 2KFG7OX2

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/2KFG7OX2MQKQNM2FHF25PU7DO5 \
  | 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: d28a6fbafa641506b3453975d7d3e37772a58bfc071683d6d4afba686b8972c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49396d4e6a93ccd927e9e53b7cedcdc9c83260111b55b684c70c9524bc6eedf7",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2018-10-12T17:13:23Z",
    "title_canon_sha256": "aafea14531cbf4c7c98306e757f69d6b369e4a04387273f4a70dbe512c984dfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.05612",
    "kind": "arxiv",
    "version": 2
  }
}