Pith Number

pith:LFIHS5W6

pith:2004:LFIHS5W63XC2CCIU4DD657XOJO

not attested not anchored not stored refs pending

An ascending HNN extension of a free group inside SL(2,C)

Danny Calegari, Nathan M. Dunfield

arxiv:math/0412136 v2 · 2004-12-07 · math.GR · 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{LFIHS5W63XC2CCIU4DD657XOJO}

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	2026-07-04T14:49:30.121161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59507976deddc5a10914e0c7eefeee4b9a0703683db35a689f5e609ea6fc2b27

Aliases

arxiv: math/0412136 · arxiv_version: math/0412136v2 · doi: 10.48550/arxiv.math/0412136 · pith_short_12: LFIHS5W63XC2 · pith_short_16: LFIHS5W63XC2CCIU · pith_short_8: LFIHS5W6

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/LFIHS5W63XC2CCIU4DD657XOJO \
  | 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: 59507976deddc5a10914e0c7eefeee4b9a0703683db35a689f5e609ea6fc2b27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a718ebf0bf3f25f9bfbf3db61717a4e3589dbb9567a3cdfc58a5d79588538c2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2004-12-07T18:41:47Z",
    "title_canon_sha256": "e5ddc2adcbb1247467c0d73d751bbac2d482d4666032181a64e812f5cd3853c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412136",
    "kind": "arxiv",
    "version": 2
  }
}