Pith Number

pith:VBPPHF36

pith:2015:VBPPHF36TH2ZHOPN7YYSI42VFV

not attested not anchored not stored refs pending

A volume-based approach to the multiplicative ergodic theorem on Banach spaces

Alex Blumenthal

arxiv:1502.06554 v2 · 2015-02-23 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VBPPHF36TH2ZHOPN7YYSI42VFV}

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	2026-05-18T01:25:15.886085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a85ef3977e99f593b9edfe312473552d54a4eb2f382eaeb8f3a0d399a83a1ce7

Aliases

arxiv: 1502.06554 · arxiv_version: 1502.06554v2 · doi: 10.48550/arxiv.1502.06554 · pith_short_12: VBPPHF36TH2Z · pith_short_16: VBPPHF36TH2ZHOPN · pith_short_8: VBPPHF36

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/VBPPHF36TH2ZHOPN7YYSI42VFV \
  | 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: a85ef3977e99f593b9edfe312473552d54a4eb2f382eaeb8f3a0d399a83a1ce7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83269a3fe8c5d7cf84bcf3023e19d08842356408c8ba52ad76f65cff27b88ce9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-02-23T19:09:41Z",
    "title_canon_sha256": "9afcd653a7e12c5fa72592f700acd0a65a2fac388ab79470e12dc85593c245bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06554",
    "kind": "arxiv",
    "version": 2
  }
}