Pith Number

pith:ORGV6UKV

pith:2026:ORGV6UKVN2ASPI4QUZX3TFWZFZ

not attested not anchored not stored refs pending

Sharp spectral Moon--Moser-type theorems in the linear range via feasible graph parameters

Yang Hu

arxiv:2607.07064 v1 · 2026-07-08 · 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{ORGV6UKVN2ASPI4QUZX3TFWZFZ}

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	2026-07-09T01:20:13.540406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

744d5f51556e8127a390a66fb996d92e5a8ce92eb2b38d1e541bc434070de605

Aliases

arxiv: 2607.07064 · arxiv_version: 2607.07064v1 · doi: 10.48550/arxiv.2607.07064 · pith_short_12: ORGV6UKVN2AS · pith_short_16: ORGV6UKVN2ASPI4Q · pith_short_8: ORGV6UKV

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/ORGV6UKVN2ASPI4QUZX3TFWZFZ \
  | 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: 744d5f51556e8127a390a66fb996d92e5a8ce92eb2b38d1e541bc434070de605

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66db6539c6899cddbdec4f50bf5bc4c408618773d0f81c99219db057f9f3cdcf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-08T06:45:25Z",
    "title_canon_sha256": "346727977fb68811ddb4de1407b541718551c5c4be93eafb1bbb43cd1d58df68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07064",
    "kind": "arxiv",
    "version": 1
  }
}