Pith Number

pith:MOCOKKQ2

pith:1993:MOCOKKQ2F5XYRSVXCT5MQ4XVGD

not attested not anchored not stored refs pending

Induced expansion for quadratic polynomials

Grzegorz Swiatek, Jacek Graczyk

arxiv:math/9308223 v1 · 1993-08-07 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MOCOKKQ2F5XYRSVXCT5MQ4XVGD}

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	2026-05-18T01:05:51.928895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6384e52a1a2f6f88cab714fac872f530d23d1fb17714750b8d0210468a671cf4

Aliases

arxiv: math/9308223 · arxiv_version: math/9308223v1 · doi: 10.48550/arxiv.math/9308223 · pith_short_12: MOCOKKQ2F5XY · pith_short_16: MOCOKKQ2F5XYRSVX · pith_short_8: MOCOKKQ2

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/MOCOKKQ2F5XYRSVXCT5MQ4XVGD \
  | 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: 6384e52a1a2f6f88cab714fac872f530d23d1fb17714750b8d0210468a671cf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a80b80c20a1148666071ca89a0781d28980905da5cdb7fe5daaa2470d9fe21a3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "1993-08-07T00:00:00Z",
    "title_canon_sha256": "3fcd72fd034ac3868c8735f80fa4eebfc6c3609761403a155b1d2fc7bab390cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9308223",
    "kind": "arxiv",
    "version": 1
  }
}