Pith Number

pith:NRHWE4H3

pith:2025:NRHWE4H32VIOSTEGIIY3DFINKC

not attested not anchored not stored refs pending

Asymptotic structure. III. Excluding a fat tree

Alex Scott, Paul Seymour, Tung Nguyen

arxiv:2509.09035 v3 · 2025-09-10 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NRHWE4H32VIOSTEGIIY3DFINKC}

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

A coarse Menger's Theorem for planar and bounded genus graphs

Receipt and verification

First computed	2026-06-11T01:09:16.716921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c4f6270fbd550e94c864231b1950d508552a44cddeb02e9d1d1fa9ebc7ed8a4

Aliases

arxiv: 2509.09035 · arxiv_version: 2509.09035v3 · doi: 10.48550/arxiv.2509.09035 · pith_short_12: NRHWE4H32VIO · pith_short_16: NRHWE4H32VIOSTEG · pith_short_8: NRHWE4H3

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/NRHWE4H32VIOSTEGIIY3DFINKC \
  | 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: 6c4f6270fbd550e94c864231b1950d508552a44cddeb02e9d1d1fa9ebc7ed8a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13ca449b4eccd358fbcfe53d205114c53da576f06dc2c2b5bac1878257511631",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-10T22:11:08Z",
    "title_canon_sha256": "7a16b1dc333478870d41eb832ec569fa46c56ed760f9d0e5f9d62c8b9cc50861"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.09035",
    "kind": "arxiv",
    "version": 3
  }
}