Pith Number

pith:7RCKEUGH

pith:2017:7RCKEUGHP6WUKG6AKYEUBKHXVR

not attested not anchored not stored refs pending

Mass and Extremals Associated with the Hardy-Schr\"odinger Operator on Hyperbolic Space

Hardy Chan, Luiz Fernando de Oliveira Faria, Nassif Ghoussoub, Saikat Mazumdar, Shaya Shakerian

arxiv:1710.01271 v2 · 2017-10-03 · 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{7RCKEUGHP6WUKG6AKYEUBKHXVR}

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	2026-05-18T00:19:08.711000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc44a250c77fad451bc0560940a8f7ac6d9e9d935807cff0e91315c15bff1335

Aliases

arxiv: 1710.01271 · arxiv_version: 1710.01271v2 · doi: 10.48550/arxiv.1710.01271 · pith_short_12: 7RCKEUGHP6WU · pith_short_16: 7RCKEUGHP6WUKG6A · pith_short_8: 7RCKEUGH

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/7RCKEUGHP6WUKG6AKYEUBKHXVR \
  | 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: fc44a250c77fad451bc0560940a8f7ac6d9e9d935807cff0e91315c15bff1335

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e463f1740c146c4255ac8b0653f8cc318897c322184539e5123d881a7533344",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-10-03T16:43:16Z",
    "title_canon_sha256": "5aec6fabddd6148cd3c1074077a0a6a7b7ccac21b302999bbdfce476b98a2a48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.01271",
    "kind": "arxiv",
    "version": 2
  }
}