Pith Number

pith:ZI352H3A

pith:2024:ZI352H3AZEYZBCZCKLQPT7AIKJ

not attested not anchored not stored refs pending

Elasticity of free type III actions of free groups

Antoine Poulin

arxiv:2412.07047 v1 · 2024-12-09 · math.GR · math.DS · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZI352H3AZEYZBCZCKLQPT7AIKJ}

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	2026-07-05T09:47:02.822023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca37dd1f60c931908b2252e0f9fc08527f906e5635a569c9ee4c6f766ec84677

Aliases

arxiv: 2412.07047 · arxiv_version: 2412.07047v1 · doi: 10.48550/arxiv.2412.07047 · pith_short_12: ZI352H3AZEYZ · pith_short_16: ZI352H3AZEYZBCZC · pith_short_8: ZI352H3A

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/ZI352H3AZEYZBCZCKLQPT7AIKJ \
  | 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: ca37dd1f60c931908b2252e0f9fc08527f906e5635a569c9ee4c6f766ec84677

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebf387ae330980f1c26b96ab05ccb2ce478f123348d1fef6beb77b4e24be01da",
    "cross_cats_sorted": [
      "math.DS",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-12-09T23:14:58Z",
    "title_canon_sha256": "5b32f1ddd6792115693686c730e3c6e95948ae3bb33622d125c9e59452678499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.07047",
    "kind": "arxiv",
    "version": 1
  }
}