Pith Number

pith:N7FQBMXN

pith:2011:N7FQBMXNQ2NGPA6XUSNIWPBJDX

not attested not anchored not stored refs pending

A geometric approach to finite rank unitary perturbations

Constanze Liaw, Ronald G. Douglas

arxiv:1110.4938 v2 · 2011-10-22 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N7FQBMXNQ2NGPA6XUSNIWPBJDX}

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	2026-05-18T02:55:20.750449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fcb00b2ed869a6783d7a49a8b3c291deae169969536fc5ee7982ac008b20d37

Aliases

arxiv: 1110.4938 · arxiv_version: 1110.4938v2 · doi: 10.48550/arxiv.1110.4938 · pith_short_12: N7FQBMXNQ2NG · pith_short_16: N7FQBMXNQ2NGPA6X · pith_short_8: N7FQBMXN

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/N7FQBMXNQ2NGPA6XUSNIWPBJDX \
  | 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: 6fcb00b2ed869a6783d7a49a8b3c291deae169969536fc5ee7982ac008b20d37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15e8e75aebfaa74939cebc8d7b504286361e606a28931125f1bf6de62ea55ab5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-22T02:47:50Z",
    "title_canon_sha256": "5f92481427e2d77c3aeffcf884dbfe648f5a92fd4d533ffe0c4b9841ec3c0742"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4938",
    "kind": "arxiv",
    "version": 2
  }
}