Pith Number

pith:5D5KVJHC

pith:2015:5D5KVJHC2PHCWYCTLOHQBNLMLH

not attested not anchored not stored refs pending

An Internal Observability Estimate for Stochastic Hyperbolic Equations

Qi Lu, Xiaoyu Fu, Xu Liu, Xu Zhang

arxiv:1511.00819 v2 · 2015-11-03 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5D5KVJHC2PHCWYCTLOHQBNLMLH}

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	2026-05-18T01:22:47.822629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8faaaa4e2d3ce2b60535b8f00b56c59fa9c65fe9c4df9711d82e53db3fbecab

Aliases

arxiv: 1511.00819 · arxiv_version: 1511.00819v2 · doi: 10.48550/arxiv.1511.00819 · pith_short_12: 5D5KVJHC2PHC · pith_short_16: 5D5KVJHC2PHCWYCT · pith_short_8: 5D5KVJHC

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/5D5KVJHC2PHCWYCTLOHQBNLMLH \
  | 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: e8faaaa4e2d3ce2b60535b8f00b56c59fa9c65fe9c4df9711d82e53db3fbecab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffa64deb2bdd6645a4c22d3e81bbe7984634c150d13cf57e073e49682a966641",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-11-03T09:07:39Z",
    "title_canon_sha256": "4e85484dfbd6248a1700fa6082cd15755981c1a7140793b2d929f364b2ee2caa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00819",
    "kind": "arxiv",
    "version": 2
  }
}