Pith Number

pith:J35ZCWPP

pith:2026:J35ZCWPPZ5DI7AVTUKFVTFY653

not attested not anchored not stored refs pending

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities

Ijay Narang, Will Perkins

arxiv:2608.03848 v1 · 2026-08-04 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J35ZCWPPZ5DI7AVTUKFVTFY653}

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	2026-08-05T01:37:14.882263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4efb9159efcf468f82b3a28b59971eeed26faa808cb05af24aabcafa40a542b9

Aliases

arxiv: 2608.03848 · arxiv_version: 2608.03848v1 · doi: 10.48550/arxiv.2608.03848 · pith_short_12: J35ZCWPPZ5DI · pith_short_16: J35ZCWPPZ5DI7AVT · pith_short_8: J35ZCWPP

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/J35ZCWPPZ5DI7AVTUKFVTFY653 \
  | 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: 4efb9159efcf468f82b3a28b59971eeed26faa808cb05af24aabcafa40a542b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebfeab3e4cbb43d14e62bddff1dd6f9b70aa1d4f2c2583a6e10d8e18460c4001",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-08-04T15:52:31Z",
    "title_canon_sha256": "9f2320493a62dd1453342b2c9413f3cc79969c0b831ef95c56132c74751112e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03848",
    "kind": "arxiv",
    "version": 1
  }
}