Pith Number

pith:VD2JZ2WG

pith:1998:VD2JZ2WGXQ62DV3WURKNMTOTYS

not attested not anchored not stored refs pending

Generic immersions of curves, knots, monodromy and gordian number

Norbert A'Campo

arxiv:math/9803081 v2 · 1998-03-18 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VD2JZ2WGXQ62DV3WURKNMTOTYS}

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

Real morsifications via the trace map

Receipt and verification

First computed	2026-07-04T14:40:28.869261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8f49ceac6bc3da1d776a454d64dd3c4a7890a50a93fabac5e74a2a67b67c046

Aliases

arxiv: math/9803081 · arxiv_version: math/9803081v2 · doi: 10.48550/arxiv.math/9803081 · pith_short_12: VD2JZ2WGXQ62 · pith_short_16: VD2JZ2WGXQ62DV3W · pith_short_8: VD2JZ2WG

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/VD2JZ2WGXQ62DV3WURKNMTOTYS \
  | 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: a8f49ceac6bc3da1d776a454d64dd3c4a7890a50a93fabac5e74a2a67b67c046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98497733620486939002e967e54b2659cc2daf6407c2a8983cd067fd84e25767",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-03-18T16:00:24Z",
    "title_canon_sha256": "688ad6a1a1bb286b84796f2d7e445d30d62dc7f6791ecddbbfba0a02dd2e5f2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9803081",
    "kind": "arxiv",
    "version": 2
  }
}