Pith Number

pith:VKKXNJVP

pith:2012:VKKXNJVPXSXNMPRVUIKN2SG6K2

not attested not anchored not stored refs pending

Rudolph's Two-Step Coding Theorem and Alpern's Lemma for R^d Actions

Anthony Quas, Ayse Sahin, Bryna Kra

arxiv:1210.5228 v3 · 2012-10-18 · 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{VKKXNJVPXSXNMPRVUIKN2SG6K2}

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	2026-05-18T02:52:14.504878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa9576a6afbcaed63e35a214dd48de5697928ac5c3cfd75d9568971e43e33a81

Aliases

arxiv: 1210.5228 · arxiv_version: 1210.5228v3 · doi: 10.48550/arxiv.1210.5228 · pith_short_12: VKKXNJVPXSXN · pith_short_16: VKKXNJVPXSXNMPRV · pith_short_8: VKKXNJVP

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/VKKXNJVPXSXNMPRVUIKN2SG6K2 \
  | 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: aa9576a6afbcaed63e35a214dd48de5697928ac5c3cfd75d9568971e43e33a81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "affdc7586cd5906d1614e25944798d9eb64eab21c7f6b671c7ce322e9b9479a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-18T19:26:26Z",
    "title_canon_sha256": "4d1ec643d04e4bdebd2a76786de17e678ca9ba7132291851d79e709f74631ffb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5228",
    "kind": "arxiv",
    "version": 3
  }
}