Pith Number

pith:6RS5JABC

pith:2026:6RS5JABCOOKKKXJT5SVYCNGLWT

not attested not anchored not stored refs pending

Occupation-condensation transition of a sublinearly vertex-reinforced random walk on regular tree

Bon A Koo, Edward Ju

arxiv:2607.16971 v1 · 2026-07-18 · cond-mat.stat-mech · math-ph · 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{6RS5JABCOOKKKXJT5SVYCNGLWT}

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	2026-07-21T01:21:08.699841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f465d480227394a55d33ecab8134cbb4fe3e8b3dc2d0229b1eca2781c297af7a

Aliases

arxiv: 2607.16971 · arxiv_version: 2607.16971v1 · doi: 10.48550/arxiv.2607.16971 · pith_short_12: 6RS5JABCOOKK · pith_short_16: 6RS5JABCOOKKKXJT · pith_short_8: 6RS5JABC

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/6RS5JABCOOKKKXJT5SVYCNGLWT \
  | 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: f465d480227394a55d33ecab8134cbb4fe3e8b3dc2d0229b1eca2781c297af7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3e6e61d3774ff281a410a0cdc6a537724297002ba8f80aa8fb4850a5da529a8",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-07-18T21:10:21Z",
    "title_canon_sha256": "4c07c71bff67e826ee7121654aada92bc2c257e034caab80d2a66a6b27a05b5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16971",
    "kind": "arxiv",
    "version": 1
  }
}