Pith Number

pith:MUTVWWBG

pith:2021:MUTVWWBGMIM3M2JYZFLP7M6JFB

not attested not anchored not stored refs pending

Profile decomposition in Sobolev spaces and decomposition of integral functionals II: homogeneous case

Mizuho Okumura

arxiv:2109.08177 v2 · 2021-09-16 · 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{MUTVWWBGMIM3M2JYZFLP7M6JFB}

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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.

Cited by

2 papers in Pith

Existence of Kelvin-Invariant Positive Solutions for Critical Elliptic Equations with Variable Coefficients via Profile Decomposition

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Receipt and verification

First computed	2026-07-05T03:56:30.933969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65275b58266219b66938c956ffb3c9285164fa4ca8b560e354fb5078ad721761

Aliases

arxiv: 2109.08177 · arxiv_version: 2109.08177v2 · doi: 10.48550/arxiv.2109.08177 · pith_short_12: MUTVWWBGMIM3 · pith_short_16: MUTVWWBGMIM3M2JY · pith_short_8: MUTVWWBG

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/MUTVWWBGMIM3M2JYZFLP7M6JFB \
  | 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: 65275b58266219b66938c956ffb3c9285164fa4ca8b560e354fb5078ad721761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d9699492f33cf32ae13d1e398749d84c220a2e5c6512491fabb2b0b61669999",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-09-16T18:18:48Z",
    "title_canon_sha256": "888cf2f2e70c2588d9ada2543f91520cb7779537f6994c02b982d24b2c179cd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.08177",
    "kind": "arxiv",
    "version": 2
  }
}