Pith Number

pith:4T4OZY7D

pith:2001:4T4OZY7DOB6DJ3YCIJ5GBZ4SBT

not attested not anchored not stored refs pending

Branched covers of tangles in three-balls

Akira Yasuhara, J\'ozef H. Przytycki, Makiko Ishiwata

arxiv:math/0109046 v1 · 2001-09-06 · 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{4T4OZY7DOB6DJ3YCIJ5GBZ4SBT}

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	2026-05-18T01:09:07.829512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f8ece3e3707c34ef02427a60e7920cc06eed134c21e203b6285de1dacbb3e4

Aliases

arxiv: math/0109046 · arxiv_version: math/0109046v1 · doi: 10.48550/arxiv.math/0109046 · pith_short_12: 4T4OZY7DOB6D · pith_short_16: 4T4OZY7DOB6DJ3YC · pith_short_8: 4T4OZY7D

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/4T4OZY7DOB6DJ3YCIJ5GBZ4SBT \
  | 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: e4f8ece3e3707c34ef02427a60e7920cc06eed134c21e203b6285de1dacbb3e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4c16d7a2146e2444e449819c7a205bdd5e6593b206bd6a0d8d22d418a5c3ef0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-09-06T20:18:24Z",
    "title_canon_sha256": "f8c0126e2f01f0f19cf4596eb6260e584afd15dc136b6923ba478a1536f37a44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0109046",
    "kind": "arxiv",
    "version": 1
  }
}