Pith Number

pith:T7TOK774

pith:2009:T7TOK774XZ5XC43NTCB24GT4EG

not attested not anchored not stored refs pending

Harmonic functions, h-transform and large deviations for random walks in random environments in dimensions four and higher

Atilla Yilmaz

arxiv:0912.1429 v3 · 2009-12-08 · 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{T7TOK774XZ5XC43NTCB24GT4EG}

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	2026-05-18T04:27:03.763162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fe6e57ffcbe7b71736d9883ae1a7c21afcdf36d5fa1f7f8443d0f0bf3b7ab30

Aliases

arxiv: 0912.1429 · arxiv_version: 0912.1429v3 · doi: 10.48550/arxiv.0912.1429 · pith_short_12: T7TOK774XZ5X · pith_short_16: T7TOK774XZ5XC43N · pith_short_8: T7TOK774

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/T7TOK774XZ5XC43NTCB24GT4EG \
  | 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: 9fe6e57ffcbe7b71736d9883ae1a7c21afcdf36d5fa1f7f8443d0f0bf3b7ab30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e62e110930c73d7e218c5cd53ccadef5709cf07d06543ca4906ff3b41daca0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-08T07:44:20Z",
    "title_canon_sha256": "8d004d02d141357e9cd19843497abd48940f7a0724a7102c9fa69ed0eddee3b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1429",
    "kind": "arxiv",
    "version": 3
  }
}