Pith Number

pith:N7D5FJZS

pith:2024:N7D5FJZSAPLCUCPSY4FWYH4M3V

not attested not anchored not stored refs pending

Critical scaling profile for trees and connected subgraphs on the complete graph

Gordon Slade, Yucheng Liu

arxiv:2412.05503 v2 · 2024-12-07 · math.PR · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N7D5FJZSAPLCUCPSY4FWYH4M3V}

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	2026-05-29T02:05:33.947215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fc7d2a73203d62a09f2c70b6c1f8cdd70b7ea1ae8597601e45a3646ccbc4f59

Aliases

arxiv: 2412.05503 · arxiv_version: 2412.05503v2 · doi: 10.48550/arxiv.2412.05503 · pith_short_12: N7D5FJZSAPLC · pith_short_16: N7D5FJZSAPLCUCPS · pith_short_8: N7D5FJZS

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/N7D5FJZSAPLCUCPSY4FWYH4M3V \
  | 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: 6fc7d2a73203d62a09f2c70b6c1f8cdd70b7ea1ae8597601e45a3646ccbc4f59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36ce4fe8a33c1ce26fe4f1be82106252a8f1760a02051c7424c998479844f35b",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-07T02:12:00Z",
    "title_canon_sha256": "703196ebf19914a161e9052355aa709c7a9ff504902dabf522aa1dea7e1e3783"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05503",
    "kind": "arxiv",
    "version": 2
  }
}