Pith Number

pith:GIPICZVU

pith:2013:GIPICZVU7ZHR5URODGHO7PPXOX

not attested not anchored not stored refs pending

Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems

Anatoly Vershik, Fedor Petrov, Pavel Zatitskiy

arxiv:1307.3523 v2 · 2013-07-12 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIPICZVU7ZHR5URODGHO7PPXOX}

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	2026-05-18T03:18:19.760078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

321e8166b4fe4f1ed22e198eefbdf775d32ab359f95a66f534a1b34fe336033f

Aliases

arxiv: 1307.3523 · arxiv_version: 1307.3523v2 · doi: 10.48550/arxiv.1307.3523 · pith_short_12: GIPICZVU7ZHR · pith_short_16: GIPICZVU7ZHR5URO · pith_short_8: GIPICZVU

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/GIPICZVU7ZHR5URODGHO7PPXOX \
  | 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: 321e8166b4fe4f1ed22e198eefbdf775d32ab359f95a66f534a1b34fe336033f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce7ce97831cb8e812dce3f125a12f0000d63d98c627ad63ed330ca2301fbce53",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-12T17:33:10Z",
    "title_canon_sha256": "2eb6542e5a2aef17a45f52453aef9f153eebfe301196d28454ba3d14088b36c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3523",
    "kind": "arxiv",
    "version": 2
  }
}