Pith Number

pith:EPFL7DBL

pith:2026:EPFL7DBL5UP3NLUG57Y44XKSA2

not attested not anchored not stored refs pending

Sets of unit fractions without two members whose average is a unit fraction

Will Sawin

arxiv:2607.15419 v1 · 2026-07-16 · math.NT · 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{EPFL7DBL5UP3NLUG57Y44XKSA2}

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	2026-07-20T00:18:32.618702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23cabf8c2bed1fb6ae86eff1ce5d5206960d40c008be880c6da76df2ef6dd189

Aliases

arxiv: 2607.15419 · arxiv_version: 2607.15419v1 · doi: 10.48550/arxiv.2607.15419 · pith_short_12: EPFL7DBL5UP3 · pith_short_16: EPFL7DBL5UP3NLUG · pith_short_8: EPFL7DBL

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/EPFL7DBL5UP3NLUG57Y44XKSA2 \
  | 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: 23cabf8c2bed1fb6ae86eff1ce5d5206960d40c008be880c6da76df2ef6dd189

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d973c0fc04c627a9a80027c780dec19be14bf186f264993b4cba4b2c86581f5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-16T19:44:56Z",
    "title_canon_sha256": "e9a83978e512ab8259ede467f41c4ee32dbae47b7f8a1b0a411b6ae8268c64fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15419",
    "kind": "arxiv",
    "version": 1
  }
}