Pith Number

pith:IBPUUBCS

pith:2025:IBPUUBCSOSOA4D2LVDBDAXQXXG

not attested not anchored not stored refs pending

The generalized Tur\'an number for K_3 in graphs without suspensions of a path on five vertices

Doudou Hei, Xinmin Hou, Yue Ma

arxiv:2509.03851 v1 · 2025-09-04 · 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{IBPUUBCSOSOA4D2LVDBDAXQXXG}

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	2026-07-05T12:04:47.917579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

405f4a0452749c0e0f4ba8c2305e17b990b601b152889451bf9b7e820dee65cd

Aliases

arxiv: 2509.03851 · arxiv_version: 2509.03851v1 · doi: 10.48550/arxiv.2509.03851 · pith_short_12: IBPUUBCSOSOA · pith_short_16: IBPUUBCSOSOA4D2L · pith_short_8: IBPUUBCS

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/IBPUUBCSOSOA4D2LVDBDAXQXXG \
  | 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: 405f4a0452749c0e0f4ba8c2305e17b990b601b152889451bf9b7e820dee65cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c66af8bc9a45bf0d28c61d26ca04846677de429fcef892f7f296ad9007084c3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-04T03:26:40Z",
    "title_canon_sha256": "6384af3dc53503d7ff4ecb0efaddf336d8a9dbeab2161a0cfd6a13ba21623ecf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.03851",
    "kind": "arxiv",
    "version": 1
  }
}