Pith Number

pith:PT5JPHDM

pith:2012:PT5JPHDMPAPLILCXHI7XOZPVOS

not attested not anchored not stored refs pending

Can you compute the operator norm?

Andreas Thom, Tim Netzer, Tobias Fritz

arxiv:1207.0975 v2 · 2012-07-04 · math.FA · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PT5JPHDMPAPLILCXHI7XOZPVOS}

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	2026-05-18T02:39:17.376479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb

Aliases

arxiv: 1207.0975 · arxiv_version: 1207.0975v2 · doi: 10.48550/arxiv.1207.0975 · pith_short_12: PT5JPHDMPAPL · pith_short_16: PT5JPHDMPAPLILCX · pith_short_8: PT5JPHDM

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/PT5JPHDMPAPLILCXHI7XOZPVOS \
  | 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: 7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c21b76b6f83dde660bc242997b3e4fd043aa73c78a7f2c1bc59ac9e5ba2b9627",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-07-04T13:30:58Z",
    "title_canon_sha256": "51d7baf16de6c966b62f575ebdff649a008ed6db8bb019f2ac1b20dd695e8d1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0975",
    "kind": "arxiv",
    "version": 2
  }
}