Pith Number

pith:CSLONO5U

pith:2026:CSLONO5UVEQG2ZVOXFC7L55BQ5

not attested not anchored not stored refs pending

A Colorful Extension of VC-dimension and Geometric Applications

Chaya Keller, Shakhar Smorodinsky

arxiv:2607.10496 v1 · 2026-07-11 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CSLONO5UVEQG2ZVOXFC7L55BQ5}

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	2026-07-14T01:21:18.421669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1496e6bbb4a9206d66aeb945f5f7a1876567deeb68467dcaaddc1c32a05e0689

Aliases

arxiv: 2607.10496 · arxiv_version: 2607.10496v1 · doi: 10.48550/arxiv.2607.10496 · pith_short_12: CSLONO5UVEQG · pith_short_16: CSLONO5UVEQG2ZVO · pith_short_8: CSLONO5U

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/CSLONO5UVEQG2ZVOXFC7L55BQ5 \
  | 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: 1496e6bbb4a9206d66aeb945f5f7a1876567deeb68467dcaaddc1c32a05e0689

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abdf1f4a731c765133e891a6fb275dcd230aa0285b887d8db2bcc1186db366aa",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-11T22:10:16Z",
    "title_canon_sha256": "4cc9780b5769a382e5278b8dfe8da5d4366c0566cbc754e6d20cd18b830c171b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10496",
    "kind": "arxiv",
    "version": 1
  }
}