Pith Number

pith:QYP7K3FO

pith:2009:QYP7K3FOF2YHVNXYW2EVK2KPGR

not attested not anchored not stored refs pending

Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity

C.H. Jeffrey Pang

arxiv:0907.5439 v5 · 2009-07-31 · 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{QYP7K3FOF2YHVNXYW2EVK2KPGR}

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	2026-05-18T04:32:19.816726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

861ff56cae2eb07ab6f8b68955694f344f567fa2d104bc1c8289598aa079eca7

Aliases

arxiv: 0907.5439 · arxiv_version: 0907.5439v5 · doi: 10.48550/arxiv.0907.5439 · pith_short_12: QYP7K3FOF2YH · pith_short_16: QYP7K3FOF2YHVNXY · pith_short_8: QYP7K3FO

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/QYP7K3FOF2YHVNXYW2EVK2KPGR \
  | 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: 861ff56cae2eb07ab6f8b68955694f344f567fa2d104bc1c8289598aa079eca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eabf72fac1ca9b682b20a380afd87669ec30a7ff03f3b2f92ea144e51ea6b4a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-07-31T18:43:19Z",
    "title_canon_sha256": "b20225ffa07597fb238b45b03982545f6a804d18965239c3d7cc49811e8d43fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5439",
    "kind": "arxiv",
    "version": 5
  }
}