Pith Number

pith:ZWY2FMCL

pith:2018:ZWY2FMCLDLR5QSAHFEGHZT4QBW

not attested not anchored not stored refs pending

Additive Volume of Sets Contained in Few Arithmetic Progressions

Christoph Spiegel, Gregory A. Freiman, Oriol Serra

arxiv:1808.08455 v1 · 2018-08-25 · 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{ZWY2FMCLDLR5QSAHFEGHZT4QBW}

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	2026-05-18T00:07:16.439061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdb1a2b04b1ae3d84807290c7ccf900d9b28081fd0181d88cc7e7db57e5ed4e2

Aliases

arxiv: 1808.08455 · arxiv_version: 1808.08455v1 · doi: 10.48550/arxiv.1808.08455 · pith_short_12: ZWY2FMCLDLR5 · pith_short_16: ZWY2FMCLDLR5QSAH · pith_short_8: ZWY2FMCL

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/ZWY2FMCLDLR5QSAHFEGHZT4QBW \
  | 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: cdb1a2b04b1ae3d84807290c7ccf900d9b28081fd0181d88cc7e7db57e5ed4e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07b30b1d86214a39e8a1fca53c48f412e52e7d3eba99742ea07ec3079476d25d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-08-25T17:45:33Z",
    "title_canon_sha256": "bc9756ce0bf403eb25c63bb0e470fbb24370be92b516c5827ae975f881690dbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08455",
    "kind": "arxiv",
    "version": 1
  }
}