Pith Number

pith:VJH2UEXE

pith:2013:VJH2UEXECA4S7JJC4KFTAKUG2V

not attested not anchored not stored refs pending

Sobolev functions on infinite-dimensional domains

Alexander V. Shaposhnikov, Andrey Yu. Pilipenko, Vladimir I. Bogachev

arxiv:1309.5475 v1 · 2013-09-21 · math.FA · 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{VJH2UEXECA4S7JJC4KFTAKUG2V}

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	2026-05-18T03:12:36.309412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa4faa12e410392fa522e28b302a86d55b619992c00c5d1be6d20ede1e2a116a

Aliases

arxiv: 1309.5475 · arxiv_version: 1309.5475v1 · doi: 10.48550/arxiv.1309.5475 · pith_short_12: VJH2UEXECA4S · pith_short_16: VJH2UEXECA4S7JJC · pith_short_8: VJH2UEXE

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/VJH2UEXECA4S7JJC4KFTAKUG2V \
  | 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: aa4faa12e410392fa522e28b302a86d55b619992c00c5d1be6d20ede1e2a116a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec0b554d7c87d266b714b78c1f8be75282ed1a9e124ca3e99059c10936d1e686",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-09-21T13:51:35Z",
    "title_canon_sha256": "24a9d8fdd950b1be4550c2152a348418bdf0a2cd564b3b953b44f29df355b132"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5475",
    "kind": "arxiv",
    "version": 1
  }
}