Pith Number

pith:Z4HH4NHD

pith:2014:Z4HH4NHDFLGZCPDNBDSGXK2VTE

not attested not anchored not stored refs pending

Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis

Mine Alsan

arxiv:1412.4261 v1 · 2014-12-13 · 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{Z4HH4NHDFLGZCPDNBDSGXK2VTE}

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	2026-05-18T02:31:19.733804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf0e7e34e32acd913c6d08e46bab5599181f2ddd924bfdb2c3e24be3e8588c3a

Aliases

arxiv: 1412.4261 · arxiv_version: 1412.4261v1 · doi: 10.48550/arxiv.1412.4261 · pith_short_12: Z4HH4NHDFLGZ · pith_short_16: Z4HH4NHDFLGZCPDN · pith_short_8: Z4HH4NHD

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/Z4HH4NHDFLGZCPDNBDSGXK2VTE \
  | 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: cf0e7e34e32acd913c6d08e46bab5599181f2ddd924bfdb2c3e24be3e8588c3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7aa33b77102c233da24ac7cb8f96bfd7f2654da5f4a2adc67b93367908607ae",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2014-12-13T17:35:08Z",
    "title_canon_sha256": "d9bd0e23c2151ff5e46768529828a42995963b84490a2af44d27b0bf3bd2396f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.4261",
    "kind": "arxiv",
    "version": 1
  }
}