Pith Number

pith:PNJUYNTJ

pith:2016:PNJUYNTJVYFPENQV2OYYO76A5D

not attested not anchored not stored refs pending

Renormalized oscillation theory for Hamiltonian systems

Fritz Gesztesy, Maxim Zinchenko

arxiv:1608.02116 v2 · 2016-08-06 · math.CA · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PNJUYNTJVYFPENQV2OYYO76A5D}

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	2026-05-18T00:46:20.842863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b534c3669ae0af23615d3b1877fc0e8c0988dd0a45cf304d10a812b50def32c

Aliases

arxiv: 1608.02116 · arxiv_version: 1608.02116v2 · doi: 10.48550/arxiv.1608.02116 · pith_short_12: PNJUYNTJVYFP · pith_short_16: PNJUYNTJVYFPENQV · pith_short_8: PNJUYNTJ

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/PNJUYNTJVYFPENQV2OYYO76A5D \
  | 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: 7b534c3669ae0af23615d3b1877fc0e8c0988dd0a45cf304d10a812b50def32c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85bfc572a67d2bcc19348cb4a054edf6e4b135c5b4d6b671ba09d33ac72bfa10",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-08-06T15:19:27Z",
    "title_canon_sha256": "7554f9686c98606327f85ff5d37c43c80bff7f84bc7eaef348ae46c54bdfe5a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02116",
    "kind": "arxiv",
    "version": 2
  }
}