Pith Number

pith:HISQGANX

pith:2024:HISQGANXZWOGIDEGOL7ALDGPXX

not attested not anchored not stored refs pending

Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis

Lorenzo Carletti

arxiv:2408.09234 v2 · 2024-08-17 · 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{HISQGANXZWOGIDEGOL7ALDGPXX}

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.

Cited by

1 paper in Pith

Localization of bubbling for high order nonlinear equations

Receipt and verification

First computed	2026-07-05T11:28:10.969454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a250301b7cd9c640c8672fe058ccfbdfd5f8d1c5985b2225b49b7dbe92af12a

Aliases

arxiv: 2408.09234 · arxiv_version: 2408.09234v2 · doi: 10.48550/arxiv.2408.09234 · pith_short_12: HISQGANXZWOG · pith_short_16: HISQGANXZWOGIDEG · pith_short_8: HISQGANX

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/HISQGANXZWOGIDEGOL7ALDGPXX \
  | 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: 3a250301b7cd9c640c8672fe058ccfbdfd5f8d1c5985b2225b49b7dbe92af12a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cb056dc6509249405e273e87654380a78f15a517aac6dace6becce3cbd570a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-08-17T15:59:52Z",
    "title_canon_sha256": "5bd1e41b34f1283c0cd115fb0a0716846e2ae05c818530a25f432ae01933196c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.09234",
    "kind": "arxiv",
    "version": 2
  }
}