Pith Number

pith:4XTIY5AS

pith:2016:4XTIY5ASXNS5PBFQJJ47QAQAMQ

not attested not anchored not stored refs pending

Characterization of Exact Lumpability for Vector Fields on Smooth Manifolds

Fatihcan M. Atay, Leonhard Horstmeyer

arxiv:1607.01237 v2 · 2016-07-05 · math.DG · math.DS · 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{4XTIY5ASXNS5PBFQJJ47QAQAMQ}

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	2026-05-18T01:11:26.506836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5e68c7412bb65d784b04a79f80200642c8ae2fc584b8ea1feebdce8aa5465dc

Aliases

arxiv: 1607.01237 · arxiv_version: 1607.01237v2 · doi: 10.48550/arxiv.1607.01237 · pith_short_12: 4XTIY5ASXNS5 · pith_short_16: 4XTIY5ASXNS5PBFQ · pith_short_8: 4XTIY5AS

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/4XTIY5ASXNS5PBFQJJ47QAQAMQ \
  | 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: e5e68c7412bb65d784b04a79f80200642c8ae2fc584b8ea1feebdce8aa5465dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b15289598b8ea65621a0eb7c73a4bcc87d262f36b3584c25d9b7162561829c48",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-07-05T13:11:29Z",
    "title_canon_sha256": "580a520db8a3c9a0e8d5176258b9cb2a07d14cfe38ad3e4bff112196edc69ed2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01237",
    "kind": "arxiv",
    "version": 2
  }
}