Pith Number

pith:5S7LZ5IL

pith:2026:5S7LZ5ILZY5S254UJIMN5TZ2EC

not attested not anchored not stored refs pending

Subquadratic growth and uniform property \(\Gamma\)

Andrew S. Toms, Ethan Kessinger

arxiv:2607.23817 v1 · 2026-07-26 · 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{5S7LZ5ILZY5S254UJIMN5TZ2EC}

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	2026-07-28T01:23:12.706801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecbebcf50bce3b2d77944a18decf3a20a76d3093a884aa6fb248c82a0882825a

Aliases

arxiv: 2607.23817 · arxiv_version: 2607.23817v1 · doi: 10.48550/arxiv.2607.23817 · pith_short_12: 5S7LZ5ILZY5S · pith_short_16: 5S7LZ5ILZY5S254U · pith_short_8: 5S7LZ5IL

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/5S7LZ5ILZY5S254UJIMN5TZ2EC \
  | 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: ecbebcf50bce3b2d77944a18decf3a20a76d3093a884aa6fb248c82a0882825a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a54f5e73977f6f10313ef02e1f4a6cf5455c02049e1a56efd1c90b4dc3acd32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-26T19:33:56Z",
    "title_canon_sha256": "fdb2d7f26ac2c50215611b4a03b991a2d8f5fdf492c4ad101217fe7e6edd79ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23817",
    "kind": "arxiv",
    "version": 1
  }
}