Pith Number

pith:MRESPPKI

pith:2024:MRESPPKIM2EAZNBEFLSGQUPQQE

not attested not anchored not stored refs pending

Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

Josh Kline, Sylvester Eriksson-Bique

arxiv:2412.02848 v1 · 2024-12-03 · math.AP · math.CA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MRESPPKIM2EAZNBEFLSGQUPQQE}

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

Medians, Oscillations, and Distance Functions

Receipt and verification

First computed	2026-07-05T09:44:20.677438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

644927bd4866880cb4242ae46851f0811acc95644acb7ff60ed36d615678328e

Aliases

arxiv: 2412.02848 · arxiv_version: 2412.02848v1 · doi: 10.48550/arxiv.2412.02848 · pith_short_12: MRESPPKIM2EA · pith_short_16: MRESPPKIM2EAZNBE · pith_short_8: MRESPPKI

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/MRESPPKIM2EAZNBEFLSGQUPQQE \
  | 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: 644927bd4866880cb4242ae46851f0811acc95644acb7ff60ed36d615678328e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d88f0a62a25f42b58819eddbc4841fcfdbc65998d5ce3bdc8361beb77270b18",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-03T21:26:14Z",
    "title_canon_sha256": "009a6bd09c50024b2cf6ceee738ab408da085206271b8f02487689e00a9db10d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.02848",
    "kind": "arxiv",
    "version": 1
  }
}