Pith Number

pith:QBOPRNDX

pith:1999:QBOPRNDXOQJKQSFXRZF3OAOWMC

not attested not anchored not stored refs pending

The instability of naked singularities in the gravitational collapse of a scalar field

Demetrios Christodoulou

arxiv:math/9901147 v1 · 1999-01-01 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QBOPRNDXOQJKQSFXRZF3OAOWMC}

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.

Cited by

3 papers in Pith

Unveiling horizons in quantum critical collapse

Classical Dressing of Timelike Naked Singularities

Unveiling horizons in quantum critical collapse

Receipt and verification

First computed	2026-05-18T01:05:33.374425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

805cf8b4777412a848b78e4bb701d6608767adf49485b3b922fb7c80feadce73

Aliases

arxiv: math/9901147 · arxiv_version: math/9901147v1 · doi: 10.48550/arxiv.math/9901147 · pith_short_12: QBOPRNDXOQJK · pith_short_16: QBOPRNDXOQJKQSFX · pith_short_8: QBOPRNDX

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/QBOPRNDXOQJKQSFXRZF3OAOWMC \
  | 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: 805cf8b4777412a848b78e4bb701d6608767adf49485b3b922fb7c80feadce73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ede07fd6e321200718c4d359d1751a1c40a420e150d63a81c0ef1f30ebdc528a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "1999-01-01T00:00:00Z",
    "title_canon_sha256": "a2bb64af18656cdcc523938c734cdeb0af9fc33e60562df622f73bfaa0f84ca3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9901147",
    "kind": "arxiv",
    "version": 1
  }
}