Pith Number

pith:7M4JLL5X

pith:2006:7M4JLL5XNYAX2MDV4FFS5D5SHJ

not attested not anchored not stored refs pending

On the unique representability of spikes over prime fields

Zhaoyang Wu, Zhi-Wei Sun

arxiv:math/0606708 v2 · 2006-06-28 · 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{7M4JLL5XNYAX2MDV4FFS5D5SHJ}

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	2026-07-04T14:55:33.792880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb3895afb76e017d3075e14b2e8fb23a7d7fd864f7692cab97e03c2891ec8797

Aliases

arxiv: math/0606708 · arxiv_version: math/0606708v2 · doi: 10.48550/arxiv.math/0606708 · pith_short_12: 7M4JLL5XNYAX · pith_short_16: 7M4JLL5XNYAX2MDV · pith_short_8: 7M4JLL5X

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/7M4JLL5XNYAX2MDV4FFS5D5SHJ \
  | 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: fb3895afb76e017d3075e14b2e8fb23a7d7fd864f7692cab97e03c2891ec8797

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc93eaf23c159dbad4435ed50c793239154c637c14c7d2bf6f708b0e83738dc2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-06-28T08:50:43Z",
    "title_canon_sha256": "1eae54e6ef85e35f64551dce4f04ec0eedb216995fed9e960f58fdc0ef3097c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606708",
    "kind": "arxiv",
    "version": 2
  }
}