Pith Number

pith:6E5S5B26

pith:2004:6E5S5B26CGE3I7ODE3VH4YSJU3

not attested not anchored not stored refs pending

On odd covering systems with distinct moduli

Song Guo, Zhi-Wei Sun

arxiv:math/0412217 v2 · 2004-12-10 · 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{6E5S5B26CGE3I7ODE3VH4YSJU3}

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	2026-07-04T14:39:27.342286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f13b2e875e1189b47dc326ea7e6249a6f027a669ff8e68ccf97b1ea4ba0dc20d

Aliases

arxiv: math/0412217 · arxiv_version: math/0412217v2 · doi: 10.48550/arxiv.math/0412217 · pith_short_12: 6E5S5B26CGE3 · pith_short_16: 6E5S5B26CGE3I7OD · pith_short_8: 6E5S5B26

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/6E5S5B26CGE3I7ODE3VH4YSJU3 \
  | 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: f13b2e875e1189b47dc326ea7e6249a6f027a669ff8e68ccf97b1ea4ba0dc20d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f217cdd2c39277324f6798af080adfd18f1fbbfea3a06da3947e8abc453bb77",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-12-10T17:51:02Z",
    "title_canon_sha256": "abcf55e4100a12a6b96b8c945066fecad1aa0e47def6ce22a0c4b0f21b662540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412217",
    "kind": "arxiv",
    "version": 2
  }
}