Pith Number

pith:Q3GF5GPR

pith:2012:Q3GF5GPRZRTUKY6PZ75PGQSGWO

not attested not anchored not stored refs pending

On the closedness of the sum of n subspaces of a Hilbert space

Ivan Feshchenko

arxiv:1201.3026 v1 · 2012-01-14 · 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{Q3GF5GPRZRTUKY6PZ75PGQSGWO}

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	2026-05-18T04:04:32.462531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86cc5e99f1cc674563cfcffaf34246b3826d81d2f54c3a0a7d3ecad8a94399f7

Aliases

arxiv: 1201.3026 · arxiv_version: 1201.3026v1 · doi: 10.48550/arxiv.1201.3026 · pith_short_12: Q3GF5GPRZRTU · pith_short_16: Q3GF5GPRZRTUKY6P · pith_short_8: Q3GF5GPR

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/Q3GF5GPRZRTUKY6PZ75PGQSGWO \
  | 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: 86cc5e99f1cc674563cfcffaf34246b3826d81d2f54c3a0a7d3ecad8a94399f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42c044c599205f33ec4c0d6c779596788ea492b5c0f6ceb555cd8d4f97e71c8d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-14T16:25:28Z",
    "title_canon_sha256": "194f8618e3fdc6bd563f20558b7dc66d2c02e2f939ae19d3cb30436fd14d2441"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3026",
    "kind": "arxiv",
    "version": 1
  }
}