Pith Number

pith:QTSFYSIJ

pith:2009:QTSFYSIJZL5SYK7FHLLP2T7S7L

not attested not anchored not stored refs pending

Sharp Bounds for Sums Associated to Graphs of Matrices

James A. Mingo (Queen's University), Roland Speicher (Queen's University)

arxiv:0909.4277 v1 · 2009-09-23 · math.OA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QTSFYSIJZL5SYK7FHLLP2T7S7L}

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	2026-05-18T03:42:32.467182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84e45c4909cafb2c2be53ad6fd4ff2fae85364d2bdfde2a6cf080fddf1a90363

Aliases

arxiv: 0909.4277 · arxiv_version: 0909.4277v1 · doi: 10.48550/arxiv.0909.4277 · pith_short_12: QTSFYSIJZL5S · pith_short_16: QTSFYSIJZL5SYK7F · pith_short_8: QTSFYSIJ

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/QTSFYSIJZL5SYK7FHLLP2T7S7L \
  | 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: 84e45c4909cafb2c2be53ad6fd4ff2fae85364d2bdfde2a6cf080fddf1a90363

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06c5f547bd51679f7d9f88cd6880597c015c50a680c98adbb2f833bf543adf8a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-09-23T19:04:56Z",
    "title_canon_sha256": "ffa319b370e334a44acb948e39b93fbdf5fbe068ce0e312544534edcd2086e28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4277",
    "kind": "arxiv",
    "version": 1
  }
}