Pith Number

pith:OBRMTCT6

pith:2012:OBRMTCT6H6JL4TH32EX62HT3FM

not attested not anchored not stored refs pending

Sharp polynomial bounds on the number of Pollicott-Ruelle resonances

Kiril Datchev, Maciej Zworski, Semyon Dyatlov

arxiv:1208.4330 v4 · 2012-08-21 · math.SP · math.AP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBRMTCT6H6JL4TH32EX62HT3FM}

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	2026-05-17T23:53:18.528733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7062c98a7e3f92be4cfbd12fed1e7b2b08637af7428334c24559c83d294f7647

Aliases

arxiv: 1208.4330 · arxiv_version: 1208.4330v4 · doi: 10.48550/arxiv.1208.4330 · pith_short_12: OBRMTCT6H6JL · pith_short_16: OBRMTCT6H6JL4TH3 · pith_short_8: OBRMTCT6

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/OBRMTCT6H6JL4TH32EX62HT3FM \
  | 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: 7062c98a7e3f92be4cfbd12fed1e7b2b08637af7428334c24559c83d294f7647

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4274eca8e73830deec5f6a1007723224a512bab46401d39b5e9be7a6018beba",
    "cross_cats_sorted": [
      "math.AP",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-08-21T18:21:32Z",
    "title_canon_sha256": "d18ecf02cabd42bf17c932481d1d20c0251a748f2fc6c075e03b7315ee2d94f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4330",
    "kind": "arxiv",
    "version": 4
  }
}