Pith Number

pith:MBFW7VF6

pith:2006:MBFW7VF62QAZZ5DDHEOSX4CBTS

not attested not anchored not stored refs pending

Estimates and structure of $\alpha$-harmonic functions

Krzysztof Bogdan, Mateusz Kwa\'snicki, Tadeusz Kulczycki

arxiv:math/0607561 v2 · 2006-07-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MBFW7VF62QAZZ5DDHEOSX4CBTS}

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	2026-05-18T00:50:48.418887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

604b6fd4bed4019cf463391d2bf0419c93b7edd9f71b2fcdc53fe8b7c6473111

Aliases

arxiv: math/0607561 · arxiv_version: math/0607561v2 · doi: 10.48550/arxiv.math/0607561 · pith_short_12: MBFW7VF62QAZ · pith_short_16: MBFW7VF62QAZZ5DD · pith_short_8: MBFW7VF6

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/MBFW7VF62QAZZ5DDHEOSX4CBTS \
  | 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: 604b6fd4bed4019cf463391d2bf0419c93b7edd9f71b2fcdc53fe8b7c6473111

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cda18ed02b68a9c5fbc67c6e027dd1601573313999e931021698ffbbcbfda3ae",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-07-22T01:36:19Z",
    "title_canon_sha256": "468766ddfed1258f74ebeb362403e7b70b9fe3f09baabb8d7b351ad807730f57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607561",
    "kind": "arxiv",
    "version": 2
  }
}