Pith Number

pith:F4X6YXXN

pith:2004:F4X6YXXN6SU3KPSFCTZALW6ATQ

not attested not anchored not stored refs pending

Problems on invariants of knots and 3-manifolds

A. Haviv, A. Kricker, A. Stoimenow, B. Sanderson, C. Lescop, C. Rourke, C.-Y. Park, D. Bar-Natan, D. Thurston, E. Ferrand, E. Guadagnini, F. Deloup, G. Masbaum, G. Massuyeau, H. Habiro, H. Murakami, H. R. Morton, J. E. Andersen, J. Murakami, J. Przytycki, J. Roberts, J. S. Carter, L. Pilo, L. Rozansky, M. Boileau, M. Goussarov, M.-J. Jeong, M. Kidwell, M. Okamoto, M. Polyak, N. Askitas, N. Dunfield, N. Okuda, N. Sato, O. Viro, R. Benedetti, R. Bott, R. Fenn, R. Kashaev, S. Baseilhac, S. Bigelow, S. Garoufalidis, S. K. Hansen, S. Morita, S. Willerton, T. Harikae, T. Kerler, T. Kohno, T. Ohtsuki, T. Stanford, T. Takata, T. T. Q. Le, V. Jones, V. Turaev, X.-S. Lin, Y. Kawahigashi, Y. Nakanishi, Y. Ohyama, Y. Shinohara, Y. Yokota

arxiv:math/0406190 v1 · 2004-06-09 · math.GT · math.AT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4X6YXXN6SU3KPSFCTZALW6ATQ}

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	2026-07-04T14:38:42.342158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f2fec5eedf4a9b53e4514f205dbc09c00db9a60ceb80749086aa753b6ec911e

Aliases

arxiv: math/0406190 · arxiv_version: math/0406190v1 · doi: 10.48550/arxiv.math/0406190 · pith_short_12: F4X6YXXN6SU3 · pith_short_16: F4X6YXXN6SU3KPSF · pith_short_8: F4X6YXXN

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/F4X6YXXN6SU3KPSFCTZALW6ATQ \
  | 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: 2f2fec5eedf4a9b53e4514f205dbc09c00db9a60ceb80749086aa753b6ec911e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7a68967264fcbe4ef231cc0b7bec252d4697f3c14de7fd26eebc48a253f93f8",
    "cross_cats_sorted": [
      "math.AT",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-06-09T15:35:57Z",
    "title_canon_sha256": "5b14cfafe71c29cf9f29d978a184837955d3dca5be4d845d80ce4c68396fa901"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406190",
    "kind": "arxiv",
    "version": 1
  }
}