Pith Number

pith:R2M67V5F

pith:2012:R2M67V5FEO4IUJETPXEXTOPV3B

not attested not anchored not stored refs pending

Nice Banach Modules and Invariant Subspaces

Stanislav Shkarin

arxiv:1209.0970 v1 · 2012-09-05 · 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{R2M67V5FEO4IUJETPXEXTOPV3B}

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	2026-05-18T03:46:15.790220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e99efd7a523b88a24937dc979b9f5d87a3b4532c52dce6c087d62262f855248

Aliases

arxiv: 1209.0970 · arxiv_version: 1209.0970v1 · doi: 10.48550/arxiv.1209.0970 · pith_short_12: R2M67V5FEO4I · pith_short_16: R2M67V5FEO4IUJET · pith_short_8: R2M67V5F

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/R2M67V5FEO4IUJETPXEXTOPV3B \
  | 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: 8e99efd7a523b88a24937dc979b9f5d87a3b4532c52dce6c087d62262f855248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a751a324d68f7994f1be26aaf886c5686d74da8f3a5528d5f27d096f978de0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-05T13:32:11Z",
    "title_canon_sha256": "79e79155ff28fb2c4b7a0b26a861fcc1fdad7b6093f8635778580650885d7c73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0970",
    "kind": "arxiv",
    "version": 1
  }
}