Pith Number

pith:NGB3IDD5

pith:2026:NGB3IDD5PSKDBYTRVUPNHUKOX7

not attested not anchored not stored refs pending

Projective-Plane Sharp States and Repulsion in Linear Crown-Free Hypergraphs

Mahesh Ramani

arxiv:2608.01568 v1 · 2026-08-03 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NGB3IDD5PSKDBYTRVUPNHUKOX7}

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	2026-08-04T02:06:00.488163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6983b40c7d7c9430e271ad1ed3d14ebfc2a424f6ea2f570ab54a23a4bb2ca2d7

Aliases

arxiv: 2608.01568 · arxiv_version: 2608.01568v1 · doi: 10.48550/arxiv.2608.01568 · pith_short_12: NGB3IDD5PSKD · pith_short_16: NGB3IDD5PSKDBYTR · pith_short_8: NGB3IDD5

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/NGB3IDD5PSKDBYTRVUPNHUKOX7 \
  | 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: 6983b40c7d7c9430e271ad1ed3d14ebfc2a424f6ea2f570ab54a23a4bb2ca2d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bad6c1d7d8d45442788a691cf24a00393c59dd29cca202a1b2a027c265bf9d75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-03T00:56:21Z",
    "title_canon_sha256": "c15b13c49ae5155ff801bc16eb0c8a41794620247768bcf2b224012cda83482c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01568",
    "kind": "arxiv",
    "version": 1
  }
}