Pith Number

pith:IFMM3II3

pith:2021:IFMM3II3J7TYJ42AJWGKPGAHRV

not attested not anchored not stored refs pending

Discrepancy in modular arithmetic progressions

Jacob Fox, Max Wenqiang Xu, Yunkun Zhou

arxiv:2104.03929 v1 · 2021-04-08 · 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{IFMM3II3J7TYJ42AJWGKPGAHRV}

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	2026-07-05T08:03:37.397709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4158cda11b4fe784f3404d8ca798078d6305b52f65c2a23b41ff0b7e4bc85a6f

Aliases

arxiv: 2104.03929 · arxiv_version: 2104.03929v1 · doi: 10.48550/arxiv.2104.03929 · pith_short_12: IFMM3II3J7TY · pith_short_16: IFMM3II3J7TYJ42A · pith_short_8: IFMM3II3

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/IFMM3II3J7TYJ42AJWGKPGAHRV \
  | 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: 4158cda11b4fe784f3404d8ca798078d6305b52f65c2a23b41ff0b7e4bc85a6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5107630ec7fb85fa987b90c44b7d77b0d164c7412d3947a8811dc1b649c4be78",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-04-08T17:20:40Z",
    "title_canon_sha256": "5a9531d36806b2ec63d915d128bbefa7796a5f9eed58a43f66df94f9051c4cee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.03929",
    "kind": "arxiv",
    "version": 1
  }
}