Pith Number

pith:2WUKMT6H

pith:2007:2WUKMT6HMGHRZ4BYCWFC2JLRYS

not attested not anchored not stored refs pending

Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2

Johannes Sjoestrand, Michael Hitrik

arxiv:math/0703394 v1 · 2007-03-13 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2WUKMT6HMGHRZ4BYCWFC2JLRYS}

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	2026-07-04T15:00:10.499569Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5a8a64fc7618f1cf038158a2d2571c4bc59d94c8fdbec50eb1ed2fabf53e7ab

Aliases

arxiv: math/0703394 · arxiv_version: math/0703394v1 · doi: 10.48550/arxiv.math/0703394 · pith_short_12: 2WUKMT6HMGHR · pith_short_16: 2WUKMT6HMGHRZ4BY · pith_short_8: 2WUKMT6H

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/2WUKMT6HMGHRZ4BYCWFC2JLRYS \
  | 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: d5a8a64fc7618f1cf038158a2d2571c4bc59d94c8fdbec50eb1ed2fabf53e7ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b28b82da9838ca6e3353967afa5748cf04a7167b3e4793aae3857390b8f7620",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2007-03-13T20:03:01Z",
    "title_canon_sha256": "b8d74843a6193f80ad0b78338fb7ff6999111fd6880d5451198d2b31f8b75579"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703394",
    "kind": "arxiv",
    "version": 1
  }
}