Pith Number

pith:XXPQE3AB

pith:2008:XXPQE3ABB63BQTROIZC4VMEKF3

not attested not anchored not stored refs pending

Liouville type results for periodic and almost periodic linear operators

Luca Rossi

arxiv:0801.2291 v2 · 2008-01-15 · 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{XXPQE3ABB63BQTROIZC4VMEKF3}

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	2026-05-18T02:16:01.874957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bddf026c010fb6184e2e4645cab08a2ee90afd9b6870f7865d722852993ddd63

Aliases

arxiv: 0801.2291 · arxiv_version: 0801.2291v2 · doi: 10.48550/arxiv.0801.2291 · pith_short_12: XXPQE3ABB63B · pith_short_16: XXPQE3ABB63BQTRO · pith_short_8: XXPQE3AB

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/XXPQE3ABB63BQTROIZC4VMEKF3 \
  | 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: bddf026c010fb6184e2e4645cab08a2ee90afd9b6870f7865d722852993ddd63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "609a0b300360ca870cf225de5f38dc01fa81bb87ce23f9bd0af52648dc442219",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-01-15T13:27:23Z",
    "title_canon_sha256": "b1a7caa07f45092c40346dc3c7d7350053379f4356b4e42c4c843f6027f51553"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.2291",
    "kind": "arxiv",
    "version": 2
  }
}