Pith Number

pith:QPKR2HP2

pith:2012:QPKR2HP2YAFS4SX7X534WGUR7N

not attested not anchored not stored refs pending

Bifurcation into spectral gaps for a noncompact semilinear Schr\"odinger equation with nonconvex potential

Christophe Troestler

arxiv:1207.1052 v1 · 2012-07-04 · 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{QPKR2HP2YAFS4SX7X534WGUR7N}

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	2026-05-18T03:51:47.641444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83d51d1dfac00b2e4affbf77cb1a91fb48b77020a956e05b790c124d8899641f

Aliases

arxiv: 1207.1052 · arxiv_version: 1207.1052v1 · doi: 10.48550/arxiv.1207.1052 · pith_short_12: QPKR2HP2YAFS · pith_short_16: QPKR2HP2YAFS4SX7 · pith_short_8: QPKR2HP2

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/QPKR2HP2YAFS4SX7X534WGUR7N \
  | 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: 83d51d1dfac00b2e4affbf77cb1a91fb48b77020a956e05b790c124d8899641f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdd372d88f342f995772abd67d7d1a9d46720d18b724f3227b2410b57409e12a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-07-04T16:28:13Z",
    "title_canon_sha256": "2f1efe78f65fc13cbd1cffdd5ce8e3de432ea004b17658ae43639ffba95dc772"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1052",
    "kind": "arxiv",
    "version": 1
  }
}