Pith Number

pith:URTGVQOG

pith:2011:URTGVQOG4JHXU7KISWCNFI7IBC

not attested not anchored not stored refs pending

Freedman's inequality for matrix martingales

Joel A. Tropp

arxiv:1101.3039 v1 · 2011-01-16 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{URTGVQOG4JHXU7KISWCNFI7IBC}

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.

Cited by

1 paper in Pith

Improved large-scale graph learning through ridge spectral sparsification

Receipt and verification

First computed	2026-05-18T02:22:57.099531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4666ac1c6e24f7a7d489584d2a3e808bfb99a576fe6a8667c9d445854e15943

Aliases

arxiv: 1101.3039 · arxiv_version: 1101.3039v1 · doi: 10.48550/arxiv.1101.3039 · pith_short_12: URTGVQOG4JHX · pith_short_16: URTGVQOG4JHXU7KI · pith_short_8: URTGVQOG

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/URTGVQOG4JHXU7KISWCNFI7IBC \
  | 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: a4666ac1c6e24f7a7d489584d2a3e808bfb99a576fe6a8667c9d445854e15943

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fe41f50e68988c1434048aabe3184de784d28d45a9b2a7690e588364cbdee32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-16T01:55:52Z",
    "title_canon_sha256": "dbf1bc129e910df82fd85ba7de467bd1dc86a9c2099637989836d320765600d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3039",
    "kind": "arxiv",
    "version": 1
  }
}