Pith Number

pith:P2JPLP3K

pith:1999:P2JPLP3KU6QPAD7Z3A5ZFQTPJV

not attested not anchored not stored refs pending

Knot Invariants and Topological Strings

Cumrun Vafa, Hirosi Ooguri

arxiv:hep-th/9912123 v3 · 1999-12-14 · 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{P2JPLP3KU6QPAD7Z3A5ZFQTPJV}

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

4 papers in Pith

Monodromy defects in Chern-Simons theory and Holography

The HZ character expansion and a hyperbolic extension of torus knots

Orientation Reversal and the Chern-Simons Natural Boundary

Bootstrapping ABJM theory

Receipt and verification

First computed	2026-07-04T15:50:00.716876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e92f5bf6aa7a0f00ff9d83b92c26f4d474cdfe838d5c798c79fc4ed47b46be1

Aliases

arxiv: hep-th/9912123 · arxiv_version: hep-th/9912123v3 · doi: 10.48550/arxiv.hep-th/9912123 · pith_short_12: P2JPLP3KU6QP · pith_short_16: P2JPLP3KU6QPAD7Z · pith_short_8: P2JPLP3K

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/P2JPLP3KU6QPAD7Z3A5ZFQTPJV \
  | 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: 7e92f5bf6aa7a0f00ff9d83b92c26f4d474cdfe838d5c798c79fc4ed47b46be1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e9187a366417cded9c12684288ee08c4f3d77707a17dddffd246ed80e99ac12",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1999-12-14T22:06:54Z",
    "title_canon_sha256": "a26e3e95383fa1c0c20b9c26844f08a3e3ce60de0aec952c36a89b295d97a396"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9912123",
    "kind": "arxiv",
    "version": 3
  }
}