Pith Number

pith:6C2AVMUT

pith:2026:6C2AVMUTM4OTCZEFBCM4JJ6JWR

not attested not anchored not stored refs pending

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials

Bernhard Heim, Johann Stumpenhusen, Steven Charlton

arxiv:2606.09545 v1 · 2026-06-08 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6C2AVMUTM4OTCZEFBCM4JJ6JWR}

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	2026-06-09T02:08:54.218918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0b40ab293671d3164850899c4a7c9b46bb9863cae662e4ead33f1b3fc271b78

Aliases

arxiv: 2606.09545 · arxiv_version: 2606.09545v1 · doi: 10.48550/arxiv.2606.09545 · pith_short_12: 6C2AVMUTM4OT · pith_short_16: 6C2AVMUTM4OTCZEF · pith_short_8: 6C2AVMUT

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/6C2AVMUTM4OTCZEFBCM4JJ6JWR \
  | 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: f0b40ab293671d3164850899c4a7c9b46bb9863cae662e4ead33f1b3fc271b78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd37513ac8e51abf7528e3bd4a0a0c81e3ee77333a924b487bda3c0cc3996356",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-08T14:26:44Z",
    "title_canon_sha256": "ac1e2699d6786e437cc6bbaac48ca11dbd47bcad5b8f69f739a18175f864c1e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09545",
    "kind": "arxiv",
    "version": 1
  }
}