Pith Number

pith:32CLJO5M

pith:2015:32CLJO5M5JC6MNZVLEIGL2RXTV

not attested not anchored not stored refs pending

On purely loxodromic actions

Ilya Kapovich

arxiv:1504.05172 v3 · 2015-04-20 · 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{32CLJO5M5JC6MNZVLEIGL2RXTV}

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	2026-05-18T01:09:07.091060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de84b4bbacea45e63735591065ea379d5f11699145e3759fa4dc30de0ddafc89

Aliases

arxiv: 1504.05172 · arxiv_version: 1504.05172v3 · doi: 10.48550/arxiv.1504.05172 · pith_short_12: 32CLJO5M5JC6 · pith_short_16: 32CLJO5M5JC6MNZV · pith_short_8: 32CLJO5M

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/32CLJO5M5JC6MNZVLEIGL2RXTV \
  | 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: de84b4bbacea45e63735591065ea379d5f11699145e3759fa4dc30de0ddafc89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41492ec0fa84b1543aa661d539972dcf13074aa9d99230e1701126bd11b0a7f4",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-04-20T19:46:53Z",
    "title_canon_sha256": "405625f48aaaf03616bff75e6a694d25da2823d6ae8b7996f430909a6fd72e2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05172",
    "kind": "arxiv",
    "version": 3
  }
}