Pith Number

pith:PQ76IASC

pith:2018:PQ76IASCHCRK2LAHRWXFLZMKS2

not attested not anchored not stored refs pending

Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series

George Tephnadze

arxiv:1803.00627 v1 · 2018-02-19 · 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{PQ76IASCHCRK2LAHRWXFLZMKS2}

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	2026-05-18T00:22:08.341127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c3fe4024238a2ad2c078dae55e58a969b0be6e6fe3285905badee78c3e09d41

Aliases

arxiv: 1803.00627 · arxiv_version: 1803.00627v1 · doi: 10.48550/arxiv.1803.00627 · pith_short_12: PQ76IASCHCRK · pith_short_16: PQ76IASCHCRK2LAH · pith_short_8: PQ76IASC

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/PQ76IASCHCRK2LAHRWXFLZMKS2 \
  | 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: 7c3fe4024238a2ad2c078dae55e58a969b0be6e6fe3285905badee78c3e09d41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f2fd1c0006344e63dfbcc1cf8630d4286f2d23c2bff0f65db785ebc511a78a1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-02-19T09:48:13Z",
    "title_canon_sha256": "7b7eaf423af9e8ae02cdbacd01f37f0992b467d290f04e0740ea42853bf7fcb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.00627",
    "kind": "arxiv",
    "version": 1
  }
}