Pith Number

pith:2HTDHPJ4

pith:2015:2HTDHPJ4R7KU5GSGI6WNRESY7J

not attested not anchored not stored refs pending

Singular Liouville Equations on $S^2$: Sharp Inequalities and Existence Results

Gabriele Mancini

arxiv:1508.02090 v1 · 2015-08-09 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HTDHPJ4R7KU5GSGI6WNRESY7J}

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	2026-05-18T01:35:34.232101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e633bd3c8fd54e9a4647acd89258fa728e21342dad44c0d460c616e97f017f

Aliases

arxiv: 1508.02090 · arxiv_version: 1508.02090v1 · doi: 10.48550/arxiv.1508.02090 · pith_short_12: 2HTDHPJ4R7KU · pith_short_16: 2HTDHPJ4R7KU5GSG · pith_short_8: 2HTDHPJ4

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/2HTDHPJ4R7KU5GSGI6WNRESY7J \
  | 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: d1e633bd3c8fd54e9a4647acd89258fa728e21342dad44c0d460c616e97f017f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df73232a0666ffeb966b1094e2704272e2deebd9516febd0cf92b94aadd353ba",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-09T22:29:04Z",
    "title_canon_sha256": "275f1e6ae28fec859b2c948e71b549617051f688e46226ba01527f17c7f5aa4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02090",
    "kind": "arxiv",
    "version": 1
  }
}