Pith Number

pith:MPFA7WQ5

pith:2019:MPFA7WQ5ZJHHJ4E7TH34W43JR2

not attested not anchored not stored refs pending

On representation formulas for solutions of linear differential equations with Caputo fractional derivatives

Mikhail Gomoyunov

arxiv:1908.08319 v1 · 2019-08-22 · math.OC · math.CA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPFA7WQ5ZJHHJ4E7TH34W43JR2}

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	2026-07-05T01:31:21.785014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63ca0fda1dca4e74f09f99f7cb73698e9ddea759335258b01f5a5b323238b8f8

Aliases

arxiv: 1908.08319 · arxiv_version: 1908.08319v1 · doi: 10.48550/arxiv.1908.08319 · pith_short_12: MPFA7WQ5ZJHH · pith_short_16: MPFA7WQ5ZJHHJ4E7 · pith_short_8: MPFA7WQ5

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/MPFA7WQ5ZJHHJ4E7TH34W43JR2 \
  | 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: 63ca0fda1dca4e74f09f99f7cb73698e9ddea759335258b01f5a5b323238b8f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17785ec797650d44e63b543761a396b508f879824874cfd495f8fe1507ab5ad4",
    "cross_cats_sorted": [
      "math.CA",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2019-08-22T11:28:03Z",
    "title_canon_sha256": "1f784a04909e8e975cdeee0d2c1e191d41bacb7275a1eb2c57a9b00d140bdc2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08319",
    "kind": "arxiv",
    "version": 1
  }
}