Pith Number

pith:FSNA6VR7

pith:2006:FSNA6VR76YVGXQJMQLOXO6GDEE

not attested not anchored not stored refs pending

Upcrossing inequalities for stationary sequences and applications

Michael Hochman

arxiv:math/0608311 v3 · 2006-08-13 · math.DS · 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{FSNA6VR76YVGXQJMQLOXO6GDEE}

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	2026-05-18T01:05:22.605875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c9a0f563ff62a6bc12c82dd7778c3211ad7fb724a9e4e8fad560985eb833da7

Aliases

arxiv: math/0608311 · arxiv_version: math/0608311v3 · doi: 10.48550/arxiv.math/0608311 · pith_short_12: FSNA6VR76YVG · pith_short_16: FSNA6VR76YVGXQJM · pith_short_8: FSNA6VR7

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/FSNA6VR76YVGXQJMQLOXO6GDEE \
  | 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: 2c9a0f563ff62a6bc12c82dd7778c3211ad7fb724a9e4e8fad560985eb833da7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad23805bef4a998be91b20ba9c9c022377115e81ad6621318b346d32d5925b64",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2006-08-13T07:41:16Z",
    "title_canon_sha256": "83c5025fdd426e0713d72a84bbf98c33eea5eb333da478e85fe97327b29b4c4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608311",
    "kind": "arxiv",
    "version": 3
  }
}