Pith Number

pith:WXHES2IO

pith:2018:WXHES2IOFIJGEJ4PXHJ4G6D5VE

not attested not anchored not stored refs pending

Extremal functions of generalized critical Hardy inequalities

Megumi Sano

arxiv:1808.00695 v1 · 2018-08-02 · 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{WXHES2IOFIJGEJ4PXHJ4G6D5VE}

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	2026-05-18T00:09:03.621675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5ce49690e2a1262278fb9d3c3787da90d8448cb08be8bdd6954850220a4a56c

Aliases

arxiv: 1808.00695 · arxiv_version: 1808.00695v1 · doi: 10.48550/arxiv.1808.00695 · pith_short_12: WXHES2IOFIJG · pith_short_16: WXHES2IOFIJGEJ4P · pith_short_8: WXHES2IO

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/WXHES2IOFIJGEJ4PXHJ4G6D5VE \
  | 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: b5ce49690e2a1262278fb9d3c3787da90d8448cb08be8bdd6954850220a4a56c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3e521b7d06ccf7b48bf6cd596f884832cfff397b1d78bca20a5a12174be788d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-08-02T07:21:27Z",
    "title_canon_sha256": "46a2163e80d290cb269e6ade6f7d528879331d4d1e5d5e32b6039dc7e86adfa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.00695",
    "kind": "arxiv",
    "version": 1
  }
}