Pith Number

pith:KKYDKJLR

pith:2015:KKYDKJLRIN2FFNQJA4EI3RUDPS

not attested not anchored not stored refs pending

Cosmological singularity theorems and splitting theorems for N-Bakry-Emery spacetimes

Eric Woolgar, William Wylie

arxiv:1509.05734 v2 · 2015-09-18 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKYDKJLRIN2FFNQJA4EI3RUDPS}

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	2026-05-18T01:20:43.041134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52b0352571437452b60907088dc6837cbb9700838a29b59661b11739b9334d84

Aliases

arxiv: 1509.05734 · arxiv_version: 1509.05734v2 · doi: 10.48550/arxiv.1509.05734 · pith_short_12: KKYDKJLRIN2F · pith_short_16: KKYDKJLRIN2FFNQJ · pith_short_8: KKYDKJLR

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/KKYDKJLRIN2FFNQJA4EI3RUDPS \
  | 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: 52b0352571437452b60907088dc6837cbb9700838a29b59661b11739b9334d84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c2586188dcb682b1d7d8c1fb69f79ed25cc3ebafa989d10b6b7280930b7c745",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-18T18:08:03Z",
    "title_canon_sha256": "cb3fee9a15375f45aca8b199240eb00fe1063cdf5b68f3dc35a8894e931dacd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05734",
    "kind": "arxiv",
    "version": 2
  }
}