Pith Number

pith:PDSAGDHN

pith:2025:PDSAGDHNV3LWOFJSJHBHOV2DVJ

not attested not anchored not stored refs pending

Resolution of two conjectures by Erd\H{o}s and Hall concerning separable numbers

Stijn Cambie, Wouter van Doorn

arxiv:2510.19727 v2 · 2025-10-22 · 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{PDSAGDHNV3LWOFJSJHBHOV2DVJ}

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	2026-05-25T02:01:08.756755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78e4030cedaed767153249c2775743aa580c2e0aef306575461678830f3c6086

Aliases

arxiv: 2510.19727 · arxiv_version: 2510.19727v2 · doi: 10.48550/arxiv.2510.19727 · pith_short_12: PDSAGDHNV3LW · pith_short_16: PDSAGDHNV3LWOFJS · pith_short_8: PDSAGDHN

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/PDSAGDHNV3LWOFJSJHBHOV2DVJ \
  | 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: 78e4030cedaed767153249c2775743aa580c2e0aef306575461678830f3c6086

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2520de1fa45733e0135a49f889d6a9171cdad2164f667504fd611d1a0cbda79f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-10-22T16:16:50Z",
    "title_canon_sha256": "2dbf817c50ce3f9b98985eed917e3302d5c9f433f4f2f7c18ca2e5134f6d073e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.19727",
    "kind": "arxiv",
    "version": 2
  }
}