Pith Number

pith:TT2JDAJA

pith:2008:TT2JDAJARKCHQENOJV7WLN5P6E

not attested not anchored not stored refs pending

On finite Thurston type orderings of braid groups

Tetsuya Ito

arxiv:0810.4074 v3 · 2008-10-22 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TT2JDAJARKCHQENOJV7WLN5P6E}

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	2026-05-18T04:33:18.299628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cf49181208a847811ae4d7f65b7aff1096c629b5d9c6c539567c988c878b97d

Aliases

arxiv: 0810.4074 · arxiv_version: 0810.4074v3 · doi: 10.48550/arxiv.0810.4074 · pith_short_12: TT2JDAJARKCH · pith_short_16: TT2JDAJARKCHQENO · pith_short_8: TT2JDAJA

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/TT2JDAJARKCHQENOJV7WLN5P6E \
  | 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: 9cf49181208a847811ae4d7f65b7aff1096c629b5d9c6c539567c988c878b97d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8dfc19174382f76f2887234023649c77809980183533753c2bbb23ef695c114",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-10-22T14:33:52Z",
    "title_canon_sha256": "25c3a738fd84212842a28050f0367425909fa6978090f8491c0fa556b73d45ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4074",
    "kind": "arxiv",
    "version": 3
  }
}