Pith Number

pith:C6P2KU6S

pith:2018:C6P2KU6S3LA6HQJ7HHRPTP65DQ

not attested not anchored not stored refs pending

Fundamental Gaps of the Fractional Schr\"odinger Operator

Changtao Sheng, Jie Shen, Weizhu Bao, Xinran Ruan

arxiv:1801.06517 v1 · 2018-01-18 · 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{C6P2KU6S3LA6HQJ7HHRPTP65DQ}

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	2026-05-18T00:25:29.820766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

179fa553d2dac1e3c13f39e2f9bfdd1c2408e7b968b6ab9b84fb22dfbd244ecb

Aliases

arxiv: 1801.06517 · arxiv_version: 1801.06517v1 · doi: 10.48550/arxiv.1801.06517 · pith_short_12: C6P2KU6S3LA6 · pith_short_16: C6P2KU6S3LA6HQJ7 · pith_short_8: C6P2KU6S

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/C6P2KU6S3LA6HQJ7HHRPTP65DQ \
  | 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: 179fa553d2dac1e3c13f39e2f9bfdd1c2408e7b968b6ab9b84fb22dfbd244ecb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c13c2d5bc5cfcffc0262f255375dc36fdd69dc802b5859f4164d97ac5de6a496",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-01-18T15:16:55Z",
    "title_canon_sha256": "840662cee5d667621aae7c9627dcebf08edc2d50fd4a25a0a0a2975772e27e68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.06517",
    "kind": "arxiv",
    "version": 1
  }
}