Pith Number

pith:OBDHSHL3

pith:2012:OBDHSHL3LCKFJXPR6FAYX7HQ3Y

not attested not anchored not stored refs pending

Submartingale Property of E_0 Under The Polarization Transformations

Emre Telatar, Mine Alsan

arxiv:1207.6788 v1 · 2012-07-29 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBDHSHL3LCKFJXPR6FAYX7HQ3Y}

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	2026-05-18T03:49:48.711511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7046791d7b589454ddf1f1418bfcf0de0cca3eb31243425cec5b4b968b9e7f2f

Aliases

arxiv: 1207.6788 · arxiv_version: 1207.6788v1 · doi: 10.48550/arxiv.1207.6788 · pith_short_12: OBDHSHL3LCKF · pith_short_16: OBDHSHL3LCKFJXPR · pith_short_8: OBDHSHL3

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/OBDHSHL3LCKFJXPR6FAYX7HQ3Y \
  | 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: 7046791d7b589454ddf1f1418bfcf0de0cca3eb31243425cec5b4b968b9e7f2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "073848f49af40d9efb81310851ed7926b61adef8c99d63c81466cc386da5422e",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-07-29T18:22:02Z",
    "title_canon_sha256": "401fd061f6f177de46a3fbf93fcdfa39b7cce0e067f29668d20c61a77e23c110"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6788",
    "kind": "arxiv",
    "version": 1
  }
}