Pith Number

pith:IO5OBU5E

pith:2000:IO5OBU5ET7JO3B5FPR6R2RJ5CJ

not attested not anchored not stored refs pending

A simple proof of the Fredholm alternative and a characterization of the Fredholm operators

A.G.Ramm

arxiv:math/0011133 v1 · 2000-11-17 · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IO5OBU5ET7JO3B5FPR6R2RJ5CJ}

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.

Cited by

1 paper in Pith

Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles

Receipt and verification

First computed	2026-07-04T14:34:55.681535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43bae0d3a49fd2ed87a57c7d1d453d126e0e7963d1b0a3376967f2290a1f7ee4

Aliases

arxiv: math/0011133 · arxiv_version: math/0011133v1 · doi: 10.48550/arxiv.math/0011133 · pith_short_12: IO5OBU5ET7JO · pith_short_16: IO5OBU5ET7JO3B5F · pith_short_8: IO5OBU5E

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/IO5OBU5ET7JO3B5FPR6R2RJ5CJ \
  | 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: 43bae0d3a49fd2ed87a57c7d1d453d126e0e7963d1b0a3376967f2290a1f7ee4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6fbfbd71c986ca49635cf802a25120cf5612092f3fcaac157c556067fdbfdd0",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2000-11-17T23:14:36Z",
    "title_canon_sha256": "29f2cd91f8db1d68192944cfc1a60103414efce5ee837fd629ca2046c3425ed2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0011133",
    "kind": "arxiv",
    "version": 1
  }
}