Pith Number

pith:FTDAXSCW

pith:2004:FTDAXSCWBUBJ77EKLEPFHUK4F7

not attested not anchored not stored refs pending

On continuous extension of grafting maps

Kentaro Ito

arxiv:math/0411133 v1 · 2004-11-06 · 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{FTDAXSCWBUBJ77EKLEPFHUK4F7}

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	2026-05-18T04:19:02.327920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cc60bc8560d029ffc8a591e53d15c2fe676310539aee18b89e9f52b65c3bdd7

Aliases

arxiv: math/0411133 · arxiv_version: math/0411133v1 · doi: 10.48550/arxiv.math/0411133 · pith_short_12: FTDAXSCWBUBJ · pith_short_16: FTDAXSCWBUBJ77EK · pith_short_8: FTDAXSCW

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/FTDAXSCWBUBJ77EKLEPFHUK4F7 \
  | 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: 2cc60bc8560d029ffc8a591e53d15c2fe676310539aee18b89e9f52b65c3bdd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4783850a38b3b1fc7a4de8e48dc6afff5f6d6031ae7e14493458cd843e053861",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-11-06T12:43:32Z",
    "title_canon_sha256": "92847ed0f7f7477670beb31ad1b3b2c282401b28b95fd28937d493b78c9f2ca1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411133",
    "kind": "arxiv",
    "version": 1
  }
}