Pith Number

pith:34HX4WBL

pith:2012:34HX4WBLSCIJ5A3HTVUQDTCU6G

not attested not anchored not stored refs pending

Every operator has almost-invariant subspaces

Adi Tcaciuc, Alexey I. Popov

arxiv:1208.5831 v1 · 2012-08-29 · 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{34HX4WBLSCIJ5A3HTVUQDTCU6G}

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	2026-05-18T03:46:48.571633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df0f7e582b90909e83679d6901cc54f1a18cc6e8683d62ce52c5ffb44c67584d

Aliases

arxiv: 1208.5831 · arxiv_version: 1208.5831v1 · doi: 10.48550/arxiv.1208.5831 · pith_short_12: 34HX4WBLSCIJ · pith_short_16: 34HX4WBLSCIJ5A3H · pith_short_8: 34HX4WBL

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/34HX4WBLSCIJ5A3HTVUQDTCU6G \
  | 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: df0f7e582b90909e83679d6901cc54f1a18cc6e8683d62ce52c5ffb44c67584d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5c215741148941d2b8427f804fe33e0ae47588ca3b878bcdf20aa6dab43d8d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-29T04:12:35Z",
    "title_canon_sha256": "bb9e7b54d99ce54c574dfa8605cbc4fac3e6ac31f120c46be381daa5c8bd92b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5831",
    "kind": "arxiv",
    "version": 1
  }
}