Pith Number

pith:MPCZWM7H

pith:2025:MPCZWM7HUSY2UCP6LNACAGLNAB

not attested not anchored not stored refs pending

Characterization of Hilbertizable spaces via convex functions

Gerd Wachsmuth, Nicolas Borchard

arxiv:2506.04686 v1 · 2025-06-05 · 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{MPCZWM7HUSY2UCP6LNACAGLNAB}

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.

Cited by

1 paper in Pith

Optimization on Weak Riemannian Manifolds

Receipt and verification

First computed	2026-07-05T11:19:07.915186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63c59b33e7a4b1aa09fe5b4020196d004444b4bcf0c6b4c59f4e978b7b7219b6

Aliases

arxiv: 2506.04686 · arxiv_version: 2506.04686v1 · doi: 10.48550/arxiv.2506.04686 · pith_short_12: MPCZWM7HUSY2 · pith_short_16: MPCZWM7HUSY2UCP6 · pith_short_8: MPCZWM7H

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/MPCZWM7HUSY2UCP6LNACAGLNAB \
  | 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: 63c59b33e7a4b1aa09fe5b4020196d004444b4bcf0c6b4c59f4e978b7b7219b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "540459d835be70e0716148348bc2644b14b3f66c85f381de952bb1c1b1fa69e7",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-06-05T07:06:28Z",
    "title_canon_sha256": "f06564b58ebc1ae2eb79946cc8424c9551b54cfd45f9024e1132df64402fba50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.04686",
    "kind": "arxiv",
    "version": 1
  }
}