Pith Number

pith:RKEBR6FF

pith:2026:RKEBR6FFYGA274W4UJNIZD3MNC

not attested not anchored not stored refs pending

No-$(k+1)$-in-line problem for $k \geqslant 3$

Alexandr Grebennikov, Anubhab Ghosal, Huy Tuan Pham, Matthew Kwan, Peter Keevash, Ritesh Goenka

arxiv:2607.05255 v1 · 2026-07-06 · 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{RKEBR6FFYGA274W4UJNIZD3MNC}

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	2026-07-07T03:19:21.209478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a8818f8a5c181aff2dca25a8c8f6c68a7f4376bf94d2712ced8795298cd88ba

Aliases

arxiv: 2607.05255 · arxiv_version: 2607.05255v1 · doi: 10.48550/arxiv.2607.05255 · pith_short_12: RKEBR6FFYGA2 · pith_short_16: RKEBR6FFYGA274W4 · pith_short_8: RKEBR6FF

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/RKEBR6FFYGA274W4UJNIZD3MNC \
  | 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: 8a8818f8a5c181aff2dca25a8c8f6c68a7f4376bf94d2712ced8795298cd88ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3bc107472456f672e3beaaa558ac7d31f7d1d7a55e0d8f389b1e873a423c28d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-06T16:01:49Z",
    "title_canon_sha256": "cb7303566097868fb0bdacd96a8810c71f6affa876d0d4b27d3c7184b44141f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05255",
    "kind": "arxiv",
    "version": 1
  }
}