Pith Number

pith:KYT7WI6Q

pith:2016:KYT7WI6QFP53CTVQW4XXMCICBB

not attested not anchored not stored refs pending

Optimal Hardy inequalities for Schr\"odinger operators on graphs

Felix Pogorzelski, Matthias Keller, Yehuda Pinchover

arxiv:1612.04051 v2 · 2016-12-13 · math.SP · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KYT7WI6QFP53CTVQW4XXMCICBB}

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	2026-05-18T00:36:19.438243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5627fb23d02bfbb14eb0b72f760902084d1b6351aa1c1567845dcaf42ab33cd8

Aliases

arxiv: 1612.04051 · arxiv_version: 1612.04051v2 · doi: 10.48550/arxiv.1612.04051 · pith_short_12: KYT7WI6QFP53 · pith_short_16: KYT7WI6QFP53CTVQ · pith_short_8: KYT7WI6Q

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/KYT7WI6QFP53CTVQW4XXMCICBB \
  | 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: 5627fb23d02bfbb14eb0b72f760902084d1b6351aa1c1567845dcaf42ab33cd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "476ce816bd3298fd68bb6a054c4936df80d0cc61074b03e9b106e461becc2426",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-12-13T07:55:01Z",
    "title_canon_sha256": "0d1c77dec28d335d80d5f546e6b495eb5aaa553f2c71250542585c263c708041"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04051",
    "kind": "arxiv",
    "version": 2
  }
}