Pith Number

pith:2H4A4YZQ

pith:2026:2H4A4YZQQ2JF2OXGPLVBY7MX5I

not attested not anchored not stored refs pending

Dense sets without large sumsets

Gabriel Dahia, Jo\~ao Pedro Marciano, Victor Souza

arxiv:2607.15269 v1 · 2026-07-16 · 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{2H4A4YZQQ2JF2OXGPLVBY7MX5I}

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	2026-07-17T01:22:17.738142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1f80e633086925d3ae67aea1c7d97ea2ac043e08304c1ac559f1b1b1b8feb68

Aliases

arxiv: 2607.15269 · arxiv_version: 2607.15269v1 · doi: 10.48550/arxiv.2607.15269 · pith_short_12: 2H4A4YZQQ2JF · pith_short_16: 2H4A4YZQQ2JF2OXG · pith_short_8: 2H4A4YZQ

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/2H4A4YZQQ2JF2OXGPLVBY7MX5I \
  | 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: d1f80e633086925d3ae67aea1c7d97ea2ac043e08304c1ac559f1b1b1b8feb68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be7c492c75ad818acc60b039cf63af772c019507b449d7d814508f2cb899aa92",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-16T17:57:34Z",
    "title_canon_sha256": "d19fe2f7c843c86872332e4a540dcc8ee8043c735e31e6c99770c164762698d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15269",
    "kind": "arxiv",
    "version": 1
  }
}