Pith Number

pith:37FMN7H3

pith:2022:37FMN7H3FDD62I6QTLYYAQ7FU7

not attested not anchored not stored refs pending

On eigenvalue problems involving the critical Hardy potential and Sobolev type inequalities with logarithmic weights in two dimensions

Futoshi Takahashi, Megumi Sano

arxiv:2210.10282 v1 · 2022-10-19 · 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{37FMN7H3FDD62I6QTLYYAQ7FU7}

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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

1 paper in Pith

Efficient Knowledge Feeding to Language Models: A Novel Integrated Encoder-Decoder Architecture

Receipt and verification

First computed	2026-07-05T05:08:08.132155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfcac6fcfb28c7ed23d09af18043e5a7e0e2f1a2bc08e363ccb6b87ab04d4878

Aliases

arxiv: 2210.10282 · arxiv_version: 2210.10282v1 · doi: 10.48550/arxiv.2210.10282 · pith_short_12: 37FMN7H3FDD6 · pith_short_16: 37FMN7H3FDD62I6Q · pith_short_8: 37FMN7H3

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/37FMN7H3FDD62I6QTLYYAQ7FU7 \
  | 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: dfcac6fcfb28c7ed23d09af18043e5a7e0e2f1a2bc08e363ccb6b87ab04d4878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13e5922ac808e6e5a38533e998723ddc5e92ee2fa1c3150a9ae6656de23ac54a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-10-19T04:03:53Z",
    "title_canon_sha256": "095c6c5adb5587cb6c3c45512d9ecdb42e17c98e988fb972b30ba7afe9348cdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.10282",
    "kind": "arxiv",
    "version": 1
  }
}