Pith Number

pith:DLGMBDEN

pith:2021:DLGMBDEN5OVTLTYFV2RYHLLTN3

not attested not anchored not stored refs pending

Discrepancy of arithmetic progressions in grids

Jacob Fox, Max Wenqiang Xu, Yunkun Zhou

arxiv:2110.15429 v1 · 2021-10-28 · math.CO · 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{DLGMBDEN5OVTLTYFV2RYHLLTN3}

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	2026-07-05T03:27:09.524216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1accc08c8debab35cf05aea383ad736edaec586b2952a81e114661e9f9f278c3

Aliases

arxiv: 2110.15429 · arxiv_version: 2110.15429v1 · doi: 10.48550/arxiv.2110.15429 · pith_short_12: DLGMBDEN5OVT · pith_short_16: DLGMBDEN5OVTLTYF · pith_short_8: DLGMBDEN

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/DLGMBDEN5OVTLTYFV2RYHLLTN3 \
  | 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: 1accc08c8debab35cf05aea383ad736edaec586b2952a81e114661e9f9f278c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "920c93ea41e3eaa588db0c6fd0659a52c2aee2e7ef51424406ae96f943b3c5ed",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-10-28T20:38:30Z",
    "title_canon_sha256": "07c1159ab7c1d96adb806f928fde220da05f4cb834cf225b8effa37a4db882ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.15429",
    "kind": "arxiv",
    "version": 1
  }
}