Pith Number

pith:KOY2WFLT

pith:2015:KOY2WFLT7QGVLM7YOYOKWYKGGE

not attested not anchored not stored refs pending

Inhomogeneous refinement equations with random affine maps

Janusz Morawiec, Rafa{\l} Kapica

arxiv:1506.07342 v1 · 2015-06-24 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KOY2WFLT7QGVLM7YOYOKWYKGGE}

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	2026-05-18T01:39:54.302231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53b1ab1573fc0d55b3f8761cab614631206b694bffbd29bacb1edaa56ad9dc80

Aliases

arxiv: 1506.07342 · arxiv_version: 1506.07342v1 · doi: 10.48550/arxiv.1506.07342 · pith_short_12: KOY2WFLT7QGV · pith_short_16: KOY2WFLT7QGVLM7Y · pith_short_8: KOY2WFLT

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/KOY2WFLT7QGVLM7YOYOKWYKGGE \
  | 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: 53b1ab1573fc0d55b3f8761cab614631206b694bffbd29bacb1edaa56ad9dc80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f216eb9ae632d23cfb404e2ff54ebe2b6e80600bd708d066e8863642d051b457",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-06-24T12:33:06Z",
    "title_canon_sha256": "f1c0755acbe64a185bbd548b6ede6b6ca75fd83e880f2a366ea69d09878b0f0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07342",
    "kind": "arxiv",
    "version": 1
  }
}