Pith Number

pith:APV4X26Z

pith:2016:APV4X26ZX6AROPZPU2O5D24UE6

not attested not anchored not stored refs pending

Note on the saturation of the norm inequalities between diamond and nuclear norm

David Gross, Martin Kliesch, Richard Kueng, Ulrich Michel

arxiv:1612.07931 v3 · 2016-12-23 · cs.IT · math.IT · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APV4X26ZX6AROPZPU2O5D24UE6}

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	2026-05-18T00:02:45.872014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ebcbebd9bf81173f2fa69dd1eb9427ad3456d16ad71d43b524429a554078da

Aliases

arxiv: 1612.07931 · arxiv_version: 1612.07931v3 · doi: 10.48550/arxiv.1612.07931 · pith_short_12: APV4X26ZX6AR · pith_short_16: APV4X26ZX6AROPZP · pith_short_8: APV4X26Z

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/APV4X26ZX6AROPZPU2O5D24UE6 \
  | 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: 03ebcbebd9bf81173f2fa69dd1eb9427ad3456d16ad71d43b524429a554078da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32e1fa7e9e1bd6437da2e8f4feab773976a0b5fbb91dde0675c66d738bc59319",
    "cross_cats_sorted": [
      "math.IT",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-12-23T10:50:45Z",
    "title_canon_sha256": "6d59e481a339be3e6649cc670bd10883a3a7ea382949995a7bec02b78f527805"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07931",
    "kind": "arxiv",
    "version": 3
  }
}