Pith Number

pith:4PVCXZHV

pith:2024:4PVCXZHVGSHSY7JH5JQOJCS6CT

not attested not anchored not stored refs pending

Infinite graph product of groups II: Analytic properties

Koichi Oyakawa

arxiv:2412.18313 v2 · 2024-12-24 · math.GR · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PVCXZHVGSHSY7JH5JQOJCS6CT}

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	2026-06-03T01:05:43.263907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3ea2be4f5348f2c7d27ea60e48a5e14c65cd2f2660496e67ad9fde8f2052df3

Aliases

arxiv: 2412.18313 · arxiv_version: 2412.18313v2 · doi: 10.48550/arxiv.2412.18313 · pith_short_12: 4PVCXZHVGSHS · pith_short_16: 4PVCXZHVGSHSY7JH · pith_short_8: 4PVCXZHV

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/4PVCXZHVGSHSY7JH5JQOJCS6CT \
  | 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: e3ea2be4f5348f2c7d27ea60e48a5e14c65cd2f2660496e67ad9fde8f2052df3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c37d77062946102964be4bd5a9eb79b9cf8e3e23833c099da48d9246a0a213a9",
    "cross_cats_sorted": [
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-12-24T09:56:00Z",
    "title_canon_sha256": "21dfd9d644ac5c671387fea20c45437dbcbd84ab7c09e7bf11a59594de4f5089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.18313",
    "kind": "arxiv",
    "version": 2
  }
}