Pith Number

pith:K42BDCSU

pith:2012:K42BDCSUBFHYOWJZPXNJQU4RY7

not attested not anchored not stored refs pending

Subgaussian concentration and rates of convergence in directed polymers

Kenneth S. Alexander, Nikos Zygouras

arxiv:1204.1819 v2 · 2012-04-09 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K42BDCSUBFHYOWJZPXNJQU4RY7}

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	2026-05-18T03:30:02.880559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5734118a54094f8759397dda985391c7e3bdc399e70ef32b37102d8ba91745f8

Aliases

arxiv: 1204.1819 · arxiv_version: 1204.1819v2 · doi: 10.48550/arxiv.1204.1819 · pith_short_12: K42BDCSUBFHY · pith_short_16: K42BDCSUBFHYOWJZ · pith_short_8: K42BDCSU

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/K42BDCSUBFHYOWJZPXNJQU4RY7 \
  | 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: 5734118a54094f8759397dda985391c7e3bdc399e70ef32b37102d8ba91745f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c373342e0eb74bd601ae66b48dda638dd5867661fdc1cbff4fa470ec80702fe3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-09T07:47:06Z",
    "title_canon_sha256": "37fb981298839fef4ea8ec08bb75ab303ef0e1662b1e1dc1d407b3efb7919d4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1819",
    "kind": "arxiv",
    "version": 2
  }
}