Pith Number

pith:WA3BR4R3

pith:2019:WA3BR4R3W7CILAV33IKFKKGR3Q

not attested not anchored not stored refs pending

Quasimode, eigenfunction and spectral projection bounds for Schr\"odinger operators on manifolds with critically singular potentials

Christopher D. Sogge, Matthew D. Blair, Yannick Sire

arxiv:1904.09665 v1 · 2019-04-21 · math.AP · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WA3BR4R3W7CILAV33IKFKKGR3Q}

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	2026-05-17T23:48:03.696071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b03618f23bb7c48582bbda145528d1dc26c56823785257d24c8c3d995c026940

Aliases

arxiv: 1904.09665 · arxiv_version: 1904.09665v1 · doi: 10.48550/arxiv.1904.09665 · pith_short_12: WA3BR4R3W7CI · pith_short_16: WA3BR4R3W7CILAV3 · pith_short_8: WA3BR4R3

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/WA3BR4R3W7CILAV33IKFKKGR3Q \
  | 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: b03618f23bb7c48582bbda145528d1dc26c56823785257d24c8c3d995c026940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "198104dcf6433af13abca3c8bf015c368daa18a16cc17f1598086fcc3af99fe4",
    "cross_cats_sorted": [
      "math.CA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-21T21:42:01Z",
    "title_canon_sha256": "257de308414675ece0a89b6275398565b8f61abcf2d21dbfbdbbfeef4913754d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.09665",
    "kind": "arxiv",
    "version": 1
  }
}