Pith Number

pith:O45WETSH

pith:2018:O45WETSHYHZOI2BKTOKJPT3SET

not attested not anchored not stored refs pending

Counterexamples to a conjecture of Harris on Hall ratio

Adam Blumenthal, Bernard Lidicky, Florian Pfender, Jan Volec, Ryan R. Martin, Sergey Norin

arxiv:1811.11116 v4 · 2018-11-27 · 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{O45WETSHYHZOI2BKTOKJPT3SET}

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	2026-07-05T00:57:48.676173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

773b624e47c1f2e4682a9b9497cf7224c906737cfa20154bd150975aeaaa5673

Aliases

arxiv: 1811.11116 · arxiv_version: 1811.11116v4 · doi: 10.48550/arxiv.1811.11116 · pith_short_12: O45WETSHYHZO · pith_short_16: O45WETSHYHZOI2BK · pith_short_8: O45WETSH

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/O45WETSHYHZOI2BKTOKJPT3SET \
  | 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: 773b624e47c1f2e4682a9b9497cf7224c906737cfa20154bd150975aeaaa5673

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f5f23f946ea8299e174e6082410e4fb97d02ca2a47f6b8463439bb4a86ba4ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-11-27T17:19:51Z",
    "title_canon_sha256": "148528d493abf69f41b8af58847ad87d7031e7edf1853c2840e75541be781381"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.11116",
    "kind": "arxiv",
    "version": 4
  }
}