Pith Number

pith:VUWFS4BC

pith:2026:VUWFS4BC46CTGWQMQRFT7ZX3AH

not attested not anchored not stored refs pending

Critical-exponent stratification and inverse realization on biregular trees

Sanghoon Kwon

arxiv:2607.21294 v1 · 2026-07-23 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VUWFS4BC46CTGWQMQRFT7ZX3AH}

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	2026-07-24T01:24:24.038801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad2c597022e785335a0c844b3fe6fb01c5880ecfe1fac18141f98dc1b37e1a78

Aliases

arxiv: 2607.21294 · arxiv_version: 2607.21294v1 · doi: 10.48550/arxiv.2607.21294 · pith_short_12: VUWFS4BC46CT · pith_short_16: VUWFS4BC46CTGWQM · pith_short_8: VUWFS4BC

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/VUWFS4BC46CTGWQMQRFT7ZX3AH \
  | 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: ad2c597022e785335a0c844b3fe6fb01c5880ecfe1fac18141f98dc1b37e1a78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06334d810013e211ca3aacdf9f53667b61c50e899fc58815fce38e860704d48c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-23T13:17:33Z",
    "title_canon_sha256": "5f664d6e01e44748fff5df17a1b22853f97a27b4edee757c4b735a0058fd7423"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21294",
    "kind": "arxiv",
    "version": 1
  }
}