Pith Number

pith:6PS67ITG

pith:2025:6PS67ITGRIZJCJZCBLVP43MWVM

not attested not anchored not stored refs pending

Volume Entropy Rigidity for Random Groups at Low Densities

Dongming Hua (Merrick)

arxiv:2505.23364 v1 · 2025-05-29 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PS67ITGRIZJCJZCBLVP43MWVM}

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	2026-07-05T11:12:00.347285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3e5efa2668a329127220aeafe6d96ab230b55bafdf7182c5162f3c35bb1d946

Aliases

arxiv: 2505.23364 · arxiv_version: 2505.23364v1 · doi: 10.48550/arxiv.2505.23364 · pith_short_12: 6PS67ITGRIZJ · pith_short_16: 6PS67ITGRIZJCJZC · pith_short_8: 6PS67ITG

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/6PS67ITGRIZJCJZCBLVP43MWVM \
  | 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: f3e5efa2668a329127220aeafe6d96ab230b55bafdf7182c5162f3c35bb1d946

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "282eac534ce4f0d7d0356a87360a80e4a8d6adc32e98771446e3afee580b5239",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-05-29T11:42:54Z",
    "title_canon_sha256": "17831defa70d2fe00a2ef2b557d389a5df8ebf29edbaf583b555fd8cf96ba3c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.23364",
    "kind": "arxiv",
    "version": 1
  }
}