Pith Number

pith:F76KT6H4

pith:2016:F76KT6H42TPRY5CMBAVNLHS6YF

not attested not anchored not stored refs pending

Multi-bump solutions for logarithmic Schr\"odinger equations

Chengxiang Zhang, Kazunaga Tanaka

arxiv:1608.01742 v2 · 2016-08-05 · 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{F76KT6H42TPRY5CMBAVNLHS6YF}

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	2026-05-18T01:04:53.343906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ffca9f8fcd4df1c744c082ad59e5ec1658f61c2b624fc9dfd293c989c7e859c

Aliases

arxiv: 1608.01742 · arxiv_version: 1608.01742v2 · doi: 10.48550/arxiv.1608.01742 · pith_short_12: F76KT6H42TPR · pith_short_16: F76KT6H42TPRY5CM · pith_short_8: F76KT6H4

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/F76KT6H42TPRY5CMBAVNLHS6YF \
  | 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: 2ffca9f8fcd4df1c744c082ad59e5ec1658f61c2b624fc9dfd293c989c7e859c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b50e6166a3b4bb16eed99b042de615ff17a299b721c5a9b578f43d0687545ef6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-05T02:32:12Z",
    "title_canon_sha256": "9e545082e625665e37ef65aaedc7415e13542866657125620e1d5638e93db44e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01742",
    "kind": "arxiv",
    "version": 2
  }
}