Pith Number

pith:APZJXV6D

pith:2011:APZJXV6D5MA4MNGWI4B4HGK3GY

not attested not anchored not stored refs pending

Singular Schrodinger operators in one dimension

E. B. Davies

arxiv:1112.4041 v1 · 2011-12-17 · math.SP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APZJXV6D5MA4MNGWI4B4HGK3GY}

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	2026-05-18T03:02:44.038419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03f29bd7c3eb01c634d64703c3995b360e066f4a82bd5a7c43dc125fa5534d3e

Aliases

arxiv: 1112.4041 · arxiv_version: 1112.4041v1 · doi: 10.48550/arxiv.1112.4041 · pith_short_12: APZJXV6D5MA4 · pith_short_16: APZJXV6D5MA4MNGW · pith_short_8: APZJXV6D

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/APZJXV6D5MA4MNGWI4B4HGK3GY \
  | 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: 03f29bd7c3eb01c634d64703c3995b360e066f4a82bd5a7c43dc125fa5534d3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e708953ae36ba183b0d15c3b1d16d0da6d27800e1eafbe642e64d1cf42d1bd6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-12-17T09:16:05Z",
    "title_canon_sha256": "86dbe75d662c2dd7289115d23ff84524fb384b1bdebbf8592aed9965e7354cc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4041",
    "kind": "arxiv",
    "version": 1
  }
}