Pith Number

pith:LDLLEY6U

pith:2025:LDLLEY6U3J5PQ5UOYVPZAIPVG7

not attested not anchored not stored refs pending

Induced rational exponents and bipartite subgraphs in $K_{s, s}$-free graphs

Hong Liu, Jun Gao, Ruonan Li, Zichao Dong

arxiv:2506.09020 v1 · 2025-06-10 · 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{LDLLEY6U3J5PQ5UOYVPZAIPVG7}

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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

Induced rational exponents near two

Receipt and verification

First computed	2026-07-05T11:19:16.791486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58d6b263d4da7af8768ec55f9021f537d73df447c6f1a41b84d63a8ea8b662df

Aliases

arxiv: 2506.09020 · arxiv_version: 2506.09020v1 · doi: 10.48550/arxiv.2506.09020 · pith_short_12: LDLLEY6U3J5P · pith_short_16: LDLLEY6U3J5PQ5UO · pith_short_8: LDLLEY6U

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/LDLLEY6U3J5PQ5UOYVPZAIPVG7 \
  | 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: 58d6b263d4da7af8768ec55f9021f537d73df447c6f1a41b84d63a8ea8b662df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9d10901958d1d58f0325a7313e14c8f4ea406b7b32c44a425b00d3da2ac61bf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-10T17:45:47Z",
    "title_canon_sha256": "9fb33381f68dec39755f5d91f60f793d2fbd60710e29df4efb222cbf62be6241"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.09020",
    "kind": "arxiv",
    "version": 1
  }
}