Pith Number

pith:ZOBQY7SP

pith:2011:ZOBQY7SPRH4FTQCW2GDPS7GXY6

not attested not anchored not stored refs pending

Monotone Operators without Enlargements

Jonathan M. Borwein, Liangjin Yao, Regina Burachik

arxiv:1110.3102 v1 · 2011-10-14 · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZOBQY7SPRH4FTQCW2GDPS7GXY6}

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	2026-05-18T04:10:58.057581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb830c7e4f89f859c056d186f97cd7c78a0ed9744b30d47ce33ad3e0324509c1

Aliases

arxiv: 1110.3102 · arxiv_version: 1110.3102v1 · doi: 10.48550/arxiv.1110.3102 · pith_short_12: ZOBQY7SPRH4F · pith_short_16: ZOBQY7SPRH4FTQCW · pith_short_8: ZOBQY7SP

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/ZOBQY7SPRH4FTQCW2GDPS7GXY6 \
  | 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: cb830c7e4f89f859c056d186f97cd7c78a0ed9744b30d47ce33ad3e0324509c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "482b47274ecf15345a2fcc378c086665212054745eb2d5f2ec985931e50066a5",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-14T01:41:42Z",
    "title_canon_sha256": "b15f0be285f9cb831202630224b5c4059d19750b33da2b7697e0d06cfc335175"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3102",
    "kind": "arxiv",
    "version": 1
  }
}