Pith Number

pith:DCCK4TCA

pith:2025:DCCK4TCAAAIEWTANYOHCY4DU5C

not attested not anchored not stored refs pending

Unavoidable pivot-minors in graphs of large rank-depth

Jungho Ahn, Kevin Hendrey, O-joung Kwon, Sang-il Oum

arxiv:2507.12697 v1 · 2025-07-17 · 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{DCCK4TCAAAIEWTANYOHCY4DU5C}

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	2026-07-05T11:38:37.516802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1884ae4c4000104b4c0dc38e2c7074e88a5710167e23c9fa8a1f776d62278850

Aliases

arxiv: 2507.12697 · arxiv_version: 2507.12697v1 · doi: 10.48550/arxiv.2507.12697 · pith_short_12: DCCK4TCAAAIE · pith_short_16: DCCK4TCAAAIEWTAN · pith_short_8: DCCK4TCA

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/DCCK4TCAAAIEWTANYOHCY4DU5C \
  | 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: 1884ae4c4000104b4c0dc38e2c7074e88a5710167e23c9fa8a1f776d62278850

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "614e8522876e4507ceb31058d3800529debf5b9513f91efa2e6a3b3a88cb8ffe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-17T00:10:48Z",
    "title_canon_sha256": "113c968bbacf785e023592a1fed702ef727820acd086f209d037a5ef21a562c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12697",
    "kind": "arxiv",
    "version": 1
  }
}