Pith Number

pith:2RI4NQFM

pith:2012:2RI4NQFMPQS7EZU2EOOUNX4JQN

not attested not anchored not stored refs pending

Sums of dilates in $\mathbb{Z}_p$

Gonzalo Fiz Pontiveros

arxiv:1203.2659 v2 · 2012-03-12 · 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{2RI4NQFMPQS7EZU2EOOUNX4JQN}

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	2026-05-18T04:00:13.133253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d451c6c0ac7c25f2669a239d46df89837bd5eb61258f9dadb7ce0dcea47d1ef8

Aliases

arxiv: 1203.2659 · arxiv_version: 1203.2659v2 · doi: 10.48550/arxiv.1203.2659 · pith_short_12: 2RI4NQFMPQS7 · pith_short_16: 2RI4NQFMPQS7EZU2 · pith_short_8: 2RI4NQFM

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/2RI4NQFMPQS7EZU2EOOUNX4JQN \
  | 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: d451c6c0ac7c25f2669a239d46df89837bd5eb61258f9dadb7ce0dcea47d1ef8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bea1483eb2064e7669c5728a96bfa8f81e2c9ce03607014875eb4c17c1df8d0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-12T21:33:25Z",
    "title_canon_sha256": "6ee370d5325340b9bbe447b59fc03f2dd283adb18b6b3702eaddfef6dbc02ae3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2659",
    "kind": "arxiv",
    "version": 2
  }
}