Pith Number

pith:2MJUUQPJ

pith:2015:2MJUUQPJSAEU64KVBHMUDJXX4Q

not attested not anchored not stored refs pending

Rational invariant tori and band edge spectra for non-selfadjoint operators

Johannes Sjoestrand, Michael Hitrik

arxiv:1502.06138 v1 · 2015-02-21 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2MJUUQPJSAEU64KVBHMUDJXX4Q}

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	2026-05-18T02:26:37.958237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3134a41e990094f715509d941a6f7e42e42077915381a9a374e016d30415738

Aliases

arxiv: 1502.06138 · arxiv_version: 1502.06138v1 · doi: 10.48550/arxiv.1502.06138 · pith_short_12: 2MJUUQPJSAEU · pith_short_16: 2MJUUQPJSAEU64KV · pith_short_8: 2MJUUQPJ

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/2MJUUQPJSAEU64KVBHMUDJXX4Q \
  | 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: d3134a41e990094f715509d941a6f7e42e42077915381a9a374e016d30415738

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b27f6ccb0dfd322ed3c02d2d072bd20498da429e73770552f0aafce85e100916",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-02-21T19:48:33Z",
    "title_canon_sha256": "cfc578f3a670a9341d096737310699dce8c78461206fe0173169d2e2e481396f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06138",
    "kind": "arxiv",
    "version": 1
  }
}