Pith Number

pith:F3RWMMFB

pith:2012:F3RWMMFBLWXOVG2AMCWCDHB62X

not attested not anchored not stored refs pending

On The Sum Of A Sobolev Space And A Weighted $L_P$-Space

Pavel Shvartsman

arxiv:1210.0592 v1 · 2012-10-01 · 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{F3RWMMFBLWXOVG2AMCWCDHB62X}

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	2026-05-18T03:44:14.853155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ee36630a15daeea9b4060ac219c3ed5de076c972b3ad2ade558362d8fc7a61b

Aliases

arxiv: 1210.0592 · arxiv_version: 1210.0592v1 · doi: 10.48550/arxiv.1210.0592 · pith_short_12: F3RWMMFBLWXO · pith_short_16: F3RWMMFBLWXOVG2A · pith_short_8: F3RWMMFB

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/F3RWMMFBLWXOVG2AMCWCDHB62X \
  | 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: 2ee36630a15daeea9b4060ac219c3ed5de076c972b3ad2ade558362d8fc7a61b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2137c1139a8846ebccf1552ebf8eb3da74f82283adb63cd4ae57c6b8e10f718e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-01T22:00:23Z",
    "title_canon_sha256": "6d5514a9022efcae650f2e04a1ff0d9551b580dda32fc6325de82b665f1adf58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0592",
    "kind": "arxiv",
    "version": 1
  }
}