Pith Number

pith:FQFPL3BN

pith:2021:FQFPL3BN5BCBPIA3B266IRYHRO

not attested not anchored not stored refs pending

Knots, Perturbative Series and Quantum Modularity

Don Zagier, Stavros Garoufalidis

arxiv:2111.06645 v3 · 2021-11-12 · math.GT · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FQFPL3BN5BCBPIA3B266IRYHRO}

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

2 papers in Pith

Orientation Reversal and the Chern-Simons Natural Boundary

$c_{\rm eff}$ from Resurgence at the Stokes Line

Receipt and verification

First computed	2026-07-05T08:35:32.943003Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c0af5ec2de84417a01b0ebde447078bbfe9a010bb46e66286b1cecb119b77e7

Aliases

arxiv: 2111.06645 · arxiv_version: 2111.06645v3 · doi: 10.48550/arxiv.2111.06645 · pith_short_12: FQFPL3BN5BCB · pith_short_16: FQFPL3BN5BCBPIA3 · pith_short_8: FQFPL3BN

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/FQFPL3BN5BCBPIA3B266IRYHRO \
  | 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: 2c0af5ec2de84417a01b0ebde447078bbfe9a010bb46e66286b1cecb119b77e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b65ae854d510a86b7ce8c4f4d82531f0880f0338d592edc4dba17367de503c",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-11-12T10:24:26Z",
    "title_canon_sha256": "fa62d6fabc6aa65c116e1447aa6c19c12caa01481b39daa050fd120b3b534f3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.06645",
    "kind": "arxiv",
    "version": 3
  }
}