Pith Number

pith:IAMEKQZP

pith:2017:IAMEKQZPJOXQG2KZVGH6DMDBMB

not attested not anchored not stored refs pending

Non-perturbative positive Lyapunov exponent of Schr\"odinger equations and its applications to skew-shift

Kai Tao

arxiv:1712.07900 v2 · 2017-12-21 · math.DS · 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{IAMEKQZPJOXQG2KZVGH6DMDBMB}

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	2026-05-18T00:17:08.104822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

401845432f4baf036959a98fe1b061606cba5c78ad8da59d5a4fca9243bfdd40

Aliases

arxiv: 1712.07900 · arxiv_version: 1712.07900v2 · doi: 10.48550/arxiv.1712.07900 · pith_short_12: IAMEKQZPJOXQ · pith_short_16: IAMEKQZPJOXQG2KZ · pith_short_8: IAMEKQZP

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/IAMEKQZPJOXQG2KZVGH6DMDBMB \
  | 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: 401845432f4baf036959a98fe1b061606cba5c78ad8da59d5a4fca9243bfdd40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2b789b438196126353fd60fcc4241dfcd70740c4f787fdd63d744172425d571",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-12-21T12:10:48Z",
    "title_canon_sha256": "d1bacefdffaef76041b84d789a52e2252da001aec22868f35c17345af5d1d83f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07900",
    "kind": "arxiv",
    "version": 2
  }
}