Pith Number

pith:MHTOIA2M

pith:2026:MHTOIA2M7LYX6SSZIRQWUT67D4

not attested not anchored not stored refs pending

Uniqueness, analyticity and mixing for Gibbs point processes via spectral gaps

Andreas G\"obel, Leon Schiller, Marcus Michelen, Marcus Pappik, Matthew Jenssen, Will Perkins

arxiv:2606.28009 v1 · 2026-06-26 · math-ph · math.MP · 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{MHTOIA2M7LYX6SSZIRQWUT67D4}

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	2026-06-29T01:14:55.070133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61e6e4034cfaf17f4a5944616a4fdf1f1d586a9fa6c511bd3a183f4c7044164a

Aliases

arxiv: 2606.28009 · arxiv_version: 2606.28009v1 · doi: 10.48550/arxiv.2606.28009 · pith_short_12: MHTOIA2M7LYX · pith_short_16: MHTOIA2M7LYX6SSZ · pith_short_8: MHTOIA2M

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/MHTOIA2M7LYX6SSZIRQWUT67D4 \
  | 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: 61e6e4034cfaf17f4a5944616a4fdf1f1d586a9fa6c511bd3a183f4c7044164a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b840963b045a14de06ba4b488118735cec45dfdccb3b9a4478c221001bef758d",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-26T12:08:10Z",
    "title_canon_sha256": "803cd2a755ac002da55262d7499232346293ca07a9f6b2f872a05f2bd2ec7bff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28009",
    "kind": "arxiv",
    "version": 1
  }
}