Pith Number

pith:7RVZF7I4

pith:2026:7RVZF7I42XCE4GBQWJQCBNRGKK

not attested not anchored not stored refs pending

Quasi-Product States and Factor Types for the One-Dimensional Hard-Core Model

Farrukh Mukhamedov, Yuri Suhov

arxiv:2606.12458 v1 · 2026-06-08 · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7RVZF7I42XCE4GBQWJQCBNRGKK}

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	2026-06-12T00:07:51.220590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc6b92fd1cd5c44e1830b26020b62652aa20acaf91dc1507b1dd374d50bf4717

Aliases

arxiv: 2606.12458 · arxiv_version: 2606.12458v1 · doi: 10.48550/arxiv.2606.12458 · pith_short_12: 7RVZF7I42XCE · pith_short_16: 7RVZF7I42XCE4GBQ · pith_short_8: 7RVZF7I4

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/7RVZF7I42XCE4GBQWJQCBNRGKK \
  | 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: fc6b92fd1cd5c44e1830b26020b62652aa20acaf91dc1507b1dd374d50bf4717

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e9759503288d4ab3a9db60accd3b41ce3e0e5809291e6faef08c89acc1f8501",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-08T04:22:52Z",
    "title_canon_sha256": "badc820073ae7fd586ce5a229d0dd4ecd1d2a531c2ac16174c85ee7a8c0c86c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12458",
    "kind": "arxiv",
    "version": 1
  }
}