Pith Number

pith:KCVHDCY7

pith:2010:KCVHDCY7LM7EK35KBMPXFEAWV4

not attested not anchored not stored refs pending

The a priori Tan Theta Theorem for spectral subspaces

Alexander K. Motovilov, Sergio Albeverio

arxiv:1012.1569 v3 · 2010-12-07 · math.SP · math-ph · math.FA · 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{KCVHDCY7LM7EK35KBMPXFEAWV4}

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	2026-05-18T03:51:14.505974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50aa718b1f5b3e456faa0b1f729016af229dc0d5a482bf7382ebaede317c2347

Aliases

arxiv: 1012.1569 · arxiv_version: 1012.1569v3 · doi: 10.48550/arxiv.1012.1569 · pith_short_12: KCVHDCY7LM7E · pith_short_16: KCVHDCY7LM7EK35K · pith_short_8: KCVHDCY7

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/KCVHDCY7LM7EK35KBMPXFEAWV4 \
  | 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: 50aa718b1f5b3e456faa0b1f729016af229dc0d5a482bf7382ebaede317c2347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c47b76961a8193e7a18ef8aeece6af7ab25053f8f85ae0e3f929b9b4bf3b9329",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-12-07T18:01:19Z",
    "title_canon_sha256": "ffb52b8d7fd4dd2fbc38ebe12dc0a76026ada99374f564d6aaaca4a2513bf27c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1569",
    "kind": "arxiv",
    "version": 3
  }
}