Pith Number

pith:ELRUKHXQ

pith:2026:ELRUKHXQ66IVBQXHE4J5NQE3YG

not attested not anchored not stored refs pending

Automorphism-invariant refinements of weakly branch actions via overlap functions

Armando Martino

arxiv:2607.26644 v1 · 2026-07-29 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ELRUKHXQ66IVBQXHE4J5NQE3YG}

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	2026-07-30T01:21:40.555770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

22e3451ef0f79150c2e72713d6c09bc19dca16ba08ee01cdb22d3bc3775adf5a

Aliases

arxiv: 2607.26644 · arxiv_version: 2607.26644v1 · doi: 10.48550/arxiv.2607.26644 · pith_short_12: ELRUKHXQ66IV · pith_short_16: ELRUKHXQ66IVBQXH · pith_short_8: ELRUKHXQ

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/ELRUKHXQ66IVBQXHE4J5NQE3YG \
  | 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: 22e3451ef0f79150c2e72713d6c09bc19dca16ba08ee01cdb22d3bc3775adf5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40571642f45cf974ecdf9d578724cc4e2012308533e0218589a17b7a6cb2efbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-29T09:05:55Z",
    "title_canon_sha256": "e5fea5ead71d442af290787a075246218067f675cb430742969d23ee1a144e11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26644",
    "kind": "arxiv",
    "version": 1
  }
}