Pith Number

pith:T5YFL2DK

pith:2018:T5YFL2DK6WTHEX5ZPIEUU2QRZ4

not attested not anchored not stored refs pending

Frames for the solution of operator equations in Hilbert spaces with fixed dual pairing

Helmut Harbrecht, Peter Balazs

arxiv:1808.06496 v1 · 2018-08-20 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T5YFL2DK6WTHEX5ZPIEUU2QRZ4}

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	2026-05-17T23:50:24.364862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f7055e86af5a6725fb97a094a6a11cf2064bfdecd28151170f0dd676457c9d5

Aliases

arxiv: 1808.06496 · arxiv_version: 1808.06496v1 · doi: 10.48550/arxiv.1808.06496 · pith_short_12: T5YFL2DK6WTH · pith_short_16: T5YFL2DK6WTHEX5Z · pith_short_8: T5YFL2DK

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/T5YFL2DK6WTHEX5ZPIEUU2QRZ4 \
  | 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: 9f7055e86af5a6725fb97a094a6a11cf2064bfdecd28151170f0dd676457c9d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87b69ad361f5470ef9251db8c54b84645bdc8894031d10b8de48bc250eabf168",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-08-20T15:04:16Z",
    "title_canon_sha256": "4431a880f229d883d79d24c44571f1651fe0cce8ff73ed9cd23616b8d9f6a77a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.06496",
    "kind": "arxiv",
    "version": 1
  }
}