Pith Number

pith:E4NFMBZV

pith:2017:E4NFMBZVSNN5W3ZH3EJ7IV7IEY

not attested not anchored not stored refs pending

Rough controls for Schroedinger operators on 2-tori

Maciej Zworski, Nicolas Burq

arxiv:1712.08635 v1 · 2017-12-22 · math.AP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E4NFMBZVSNN5W3ZH3EJ7IV7IEY}

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	2026-05-18T00:27:17.158855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

271a560735935bdb6f27d913f457e8261d0f5e06edfb323cca66c82e7f741804

Aliases

arxiv: 1712.08635 · arxiv_version: 1712.08635v1 · doi: 10.48550/arxiv.1712.08635 · pith_short_12: E4NFMBZVSNN5 · pith_short_16: E4NFMBZVSNN5W3ZH · pith_short_8: E4NFMBZV

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/E4NFMBZVSNN5W3ZH3EJ7IV7IEY \
  | 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: 271a560735935bdb6f27d913f457e8261d0f5e06edfb323cca66c82e7f741804

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7252f9df0f3ca811ffbda179681ef73608f128f70bd455cbc3408894654ec9e",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-12-22T19:56:04Z",
    "title_canon_sha256": "cbd0ae0c211d32b2a0f286414b9dc16ad2aaf3e3cd62c511f5de089b4775cc7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.08635",
    "kind": "arxiv",
    "version": 1
  }
}