Pith Number

pith:BQG2GLYW

pith:2016:BQG2GLYWXI5V72XQINZI6Y6KUP

not attested not anchored not stored refs pending

Relaxation and Purification for Nonconvex Variational Problems in Dual Banach Spaces: The Minimization Principle in Saturated Measure Spaces

Nobusumi Sagara

arxiv:1604.02514 v3 · 2016-04-09 · 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{BQG2GLYWXI5V72XQINZI6Y6KUP}

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	2026-05-18T00:45:02.713453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c0da32f16ba3b5feaf043728f63caa3c309e5f2b90fca0afca5e48beaf6331d

Aliases

arxiv: 1604.02514 · arxiv_version: 1604.02514v3 · doi: 10.48550/arxiv.1604.02514 · pith_short_12: BQG2GLYWXI5V · pith_short_16: BQG2GLYWXI5V72XQ · pith_short_8: BQG2GLYW

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/BQG2GLYWXI5V72XQINZI6Y6KUP \
  | 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: 0c0da32f16ba3b5feaf043728f63caa3c309e5f2b90fca0afca5e48beaf6331d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09481f1381846eba514acdfc6e792c2ad9d481d20b6156c2325c9180753331e2",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-04-09T02:38:38Z",
    "title_canon_sha256": "f1c8c11ee31f78e23f6a1d4c4bf4fd650f89af53b16fa57590c034a07e8a8768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02514",
    "kind": "arxiv",
    "version": 3
  }
}