Pith Number

pith:AWZKNDVX

pith:2026:AWZKNDVXDADHL55RNXVBUUFGJU

not attested not anchored not stored refs pending

Collisions of random walks in unimodular random graphs: applications to the random geometric graph and long-range percolation

Carlos Martinez-Arevalo, Jhon Astoquillca

arxiv:2607.04002 v1 · 2026-07-04 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AWZKNDVXDADHL55RNXVBUUFGJU}

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	2026-07-07T02:18:52.591371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05b2a68eb7180675f7b16dea1a50a64d137ab45e7ff15cd6c5c198f5f733c8cf

Aliases

arxiv: 2607.04002 · arxiv_version: 2607.04002v1 · doi: 10.48550/arxiv.2607.04002 · pith_short_12: AWZKNDVXDADH · pith_short_16: AWZKNDVXDADHL55R · pith_short_8: AWZKNDVX

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/AWZKNDVXDADHL55RNXVBUUFGJU \
  | 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: 05b2a68eb7180675f7b16dea1a50a64d137ab45e7ff15cd6c5c198f5f733c8cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d99d46da150383f4914438956cf22db4c1e97524b6450a5d4af1d53252700cd9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-04T19:52:03Z",
    "title_canon_sha256": "e8ef57bc01a3fc1adf7a5764efe53720ee2e59f2baa67541c2d3cbc09d10552f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04002",
    "kind": "arxiv",
    "version": 1
  }
}