Pith Number

pith:GRXDX4KH

pith:2016:GRXDX4KH7JFVTMKNFXYQGYXIVM

not attested not anchored not stored refs pending

Invariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillators

Albert Granados

arxiv:1609.03215 v3 · 2016-09-11 · 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{GRXDX4KH7JFVTMKNFXYQGYXIVM}

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	2026-05-18T00:41:39.192081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

346e3bf147fa4b59b14d2df10362e8ab33e5ec1134c189feb2fe41cce25032ab

Aliases

arxiv: 1609.03215 · arxiv_version: 1609.03215v3 · doi: 10.48550/arxiv.1609.03215 · pith_short_12: GRXDX4KH7JFV · pith_short_16: GRXDX4KH7JFVTMKN · pith_short_8: GRXDX4KH

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/GRXDX4KH7JFVTMKNFXYQGYXIVM \
  | 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: 346e3bf147fa4b59b14d2df10362e8ab33e5ec1134c189feb2fe41cce25032ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ed0c6c0aa199ba7caacacb9fc486f4efd3b58c5edc4ced569429138bfbbb04a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-09-11T21:22:00Z",
    "title_canon_sha256": "6b0c16fe43620cc3deca004d9086021935af8b8507bfa86d691d05769200247a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03215",
    "kind": "arxiv",
    "version": 3
  }
}