Pith Number

pith:AB55MXGJ

pith:2010:AB55MXGJ3CUBLR6B5E3PMV2JJD

not attested not anchored not stored refs pending

Classifying Complemented Subspaces of $L_p$ with Alspach Norm

Isaac DeFrain, Mitch Phillipson, Simei Tong

arxiv:1004.5341 v1 · 2010-04-29 · 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{AB55MXGJ3CUBLR6B5E3PMV2JJD}

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	2026-05-18T02:24:14.936727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

007bd65cc9d8a815c7c1e936f6574948d270768900d883a49a38270b2f73089b

Aliases

arxiv: 1004.5341 · arxiv_version: 1004.5341v1 · doi: 10.48550/arxiv.1004.5341 · pith_short_12: AB55MXGJ3CUB · pith_short_16: AB55MXGJ3CUBLR6B · pith_short_8: AB55MXGJ

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/AB55MXGJ3CUBLR6B5E3PMV2JJD \
  | 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: 007bd65cc9d8a815c7c1e936f6574948d270768900d883a49a38270b2f73089b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "198dcc2e70dc5840f165658f01ccc12994c6ad9ac4b1efea9f216ebdea4fe6ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-04-29T17:01:21Z",
    "title_canon_sha256": "25d7fcf8287b7be79c417c0748a9563722842763ad7a535a6ddf74241581f179"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5341",
    "kind": "arxiv",
    "version": 1
  }
}