Pith Number

pith:F33YXCIJ

pith:2010:F33YXCIJ33KOOMFRUK4PMU5CSU

not attested not anchored not stored refs pending

The inclusion relation between Sobolev and modulation spaces

Masaharu Kobayashi, Mitsuru Sugimoto

arxiv:1009.0895 v2 · 2010-09-05 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F33YXCIJ33KOOMFRUK4PMU5CSU}

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	2026-05-18T04:41:14.903737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ef78b8909ded4e730b1a2b8f653a2950b9a19b5f9930a9495a8abf5a84e52a6

Aliases

arxiv: 1009.0895 · arxiv_version: 1009.0895v2 · doi: 10.48550/arxiv.1009.0895 · pith_short_12: F33YXCIJ33KO · pith_short_16: F33YXCIJ33KOOMFR · pith_short_8: F33YXCIJ

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/F33YXCIJ33KOOMFRUK4PMU5CSU \
  | 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: 2ef78b8909ded4e730b1a2b8f653a2950b9a19b5f9930a9495a8abf5a84e52a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f543cd828688169ffdd4dce4e3a103a88015656a921f9e029647f43945e9a1b3",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-09-05T07:37:10Z",
    "title_canon_sha256": "203f146e56cc20aa7ce1be562863a05b38bf645e37c307050129066dbd9e50c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0895",
    "kind": "arxiv",
    "version": 2
  }
}