Pith Number

pith:W2D5DK7N

pith:2015:W2D5DK7NHTYVZ4WCSNBX3BOMOC

not attested not anchored not stored refs pending

The Bohr--P\'al Theorem and the Sobolev Space $W_2^{1/2}$

Vladimir Lebedev

arxiv:1508.07167 v1 · 2015-08-28 · 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{W2D5DK7NHTYVZ4WCSNBX3BOMOC}

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	2026-05-18T01:20:55.831086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b687d1abed3cf15cf2c293437d85cc70902a9a21ebf3edd33fc32703c4983309

Aliases

arxiv: 1508.07167 · arxiv_version: 1508.07167v1 · doi: 10.48550/arxiv.1508.07167 · pith_short_12: W2D5DK7NHTYV · pith_short_16: W2D5DK7NHTYVZ4WC · pith_short_8: W2D5DK7N

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/W2D5DK7NHTYVZ4WCSNBX3BOMOC \
  | 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: b687d1abed3cf15cf2c293437d85cc70902a9a21ebf3edd33fc32703c4983309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f029db6559906a7920090632e3fac9ba70437e9e535a38bf2fa6f1e47d8221aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-28T10:58:36Z",
    "title_canon_sha256": "29dfcdd5aa16bae211a3499bd86c07aa805ec2c2b05ddc819ad4a8b54c15b1d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07167",
    "kind": "arxiv",
    "version": 1
  }
}