Pith Number

pith:RV47YH7A

pith:2025:RV47YH7ASD3VYR3UPGJBPYZEWJ

not attested not anchored not stored refs pending

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

Shengtong Zhang

arxiv:2507.10037 v1 · 2025-07-14 · math.CO · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RV47YH7ASD3VYR3UPGJBPYZEWJ}

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.

Cited by

1 paper in Pith

Beyond the MaxCut problem in $H$-free graphs

Receipt and verification

First computed	2026-07-05T11:36:43.978848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d79fc1fe090f75c4774799217e324b2472f99b37370b07b4505d05801ef6005

Aliases

arxiv: 2507.10037 · arxiv_version: 2507.10037v1 · doi: 10.48550/arxiv.2507.10037 · pith_short_12: RV47YH7ASD3V · pith_short_16: RV47YH7ASD3VYR3U · pith_short_8: RV47YH7A

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/RV47YH7ASD3VYR3UPGJBPYZEWJ \
  | 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: 8d79fc1fe090f75c4774799217e324b2472f99b37370b07b4505d05801ef6005

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e42ccbb1e9315a3022f20dd6bc41ffefaa20118b259a410785c8fef61cd1bd13",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-14T08:15:11Z",
    "title_canon_sha256": "c799685a1c9b69642ec289380d3c787f37dd74a9f6a6a02cd025d0801294c89e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.10037",
    "kind": "arxiv",
    "version": 1
  }
}