Pith Number

pith:OIF4YA3H

pith:2005:OIF4YA3HY652VCP6XO7VY6CXLP

not attested not anchored not stored refs pending

Generalized $\alpha$-variation and Lebesgue equivalence to differentiable functions

Jakub Duda

arxiv:math/0512428 v2 · 2005-12-18 · 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{OIF4YA3HY652VCP6XO7VY6CXLP}

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	2026-07-04T15:13:12.153595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

720bcc0367c7bbaa89febbbf5c78575bc4413ecf0fc72949d5ef0bc6d63c9012

Aliases

arxiv: math/0512428 · arxiv_version: math/0512428v2 · doi: 10.48550/arxiv.math/0512428 · pith_short_12: OIF4YA3HY652 · pith_short_16: OIF4YA3HY652VCP6 · pith_short_8: OIF4YA3H

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/OIF4YA3HY652VCP6XO7VY6CXLP \
  | 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: 720bcc0367c7bbaa89febbbf5c78575bc4413ecf0fc72949d5ef0bc6d63c9012

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ade2ef314840a2a4b0f2a87a0f0a7a1e8f8dc177bbee0bbfd2a606d58ea86448",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2005-12-18T17:12:33Z",
    "title_canon_sha256": "459eb2f04aef9f80ce5eccedc5061d4853098fd7585caa142132beaab331dd69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512428",
    "kind": "arxiv",
    "version": 2
  }
}