Pith Number

pith:VE64EYGK

pith:2026:VE64EYGKSCGGPJPUO7YLZH6XVS

not attested not anchored not stored refs pending

The structure of solution spaces for fractional-order operators, with gradient estimates

Gerd Grubb

arxiv:2607.02312 v1 · 2026-07-02 · math.AP · 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{VE64EYGKSCGGPJPUO7YLZH6XVS}

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	2026-07-03T01:17:48.158053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a93dc260ca908c67a5f477f0bc9fd7ac97c1fcfa4fccd55458a10104bcee6256

Aliases

arxiv: 2607.02312 · arxiv_version: 2607.02312v1 · doi: 10.48550/arxiv.2607.02312 · pith_short_12: VE64EYGKSCGG · pith_short_16: VE64EYGKSCGGPJPU · pith_short_8: VE64EYGK

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/VE64EYGKSCGGPJPUO7YLZH6XVS \
  | 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: a93dc260ca908c67a5f477f0bc9fd7ac97c1fcfa4fccd55458a10104bcee6256

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6594c4c2c328179680097833ef53cb1adc7a2b9b44651b5dc78143654abbf8fa",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-02T15:24:53Z",
    "title_canon_sha256": "026d92d799c13bf0ba38ff8dfcb492ccb4ddcc8a8334038240d1747b46386963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02312",
    "kind": "arxiv",
    "version": 1
  }
}