Pith Number

pith:IBZP745S

pith:2019:IBZP745SPOHOSLWXIMOBXJVJJX

not attested not anchored not stored refs pending

The Littlewood-Offord Problem for Markov Chains

Shravas Rao

arxiv:1904.13019 v1 · 2019-04-30 · math.CO · cs.CC · 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{IBZP745SPOHOSLWXIMOBXJVJJX}

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	2026-05-17T23:47:24.177901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4072fff3b27b8ee92ed7431c1ba6a94dfe9a403a2ab1d1bf980876af488202e0

Aliases

arxiv: 1904.13019 · arxiv_version: 1904.13019v1 · doi: 10.48550/arxiv.1904.13019 · pith_short_12: IBZP745SPOHO · pith_short_16: IBZP745SPOHOSLWX · pith_short_8: IBZP745S

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/IBZP745SPOHOSLWXIMOBXJVJJX \
  | 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: 4072fff3b27b8ee92ed7431c1ba6a94dfe9a403a2ab1d1bf980876af488202e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd430a3328dc064f0c1810105944d5bdad7f6c9c567b6fa38f9a4e1b9adb2db6",
    "cross_cats_sorted": [
      "cs.CC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-30T02:22:39Z",
    "title_canon_sha256": "1be858f63e4dda4ce39cfc1394e735362dc633c97ba3864020cdec956365610c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.13019",
    "kind": "arxiv",
    "version": 1
  }
}