Pith Number

pith:PHVE4KYD

pith:2015:PHVE4KYDO5EWM2MCGCUCHAJICN

not attested not anchored not stored refs pending

Degeneracies of parametric lens model families near folds and cusps

Jenny Wagner, Matthias Bartelmann

arxiv:1512.05095 v1 · 2015-12-16 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHVE4KYDO5EWM2MCGCUCHAJICN}

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	2026-05-18T01:24:13.507667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ea4e2b03774966698230a82381281376e56f05ccb479fb14328b00c0d85e4c

Aliases

arxiv: 1512.05095 · arxiv_version: 1512.05095v1 · doi: 10.48550/arxiv.1512.05095 · pith_short_12: PHVE4KYDO5EW · pith_short_16: PHVE4KYDO5EWM2MC · pith_short_8: PHVE4KYD

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/PHVE4KYDO5EWM2MCGCUCHAJICN \
  | 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: 79ea4e2b03774966698230a82381281376e56f05ccb479fb14328b00c0d85e4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f795a43271d845d8c42e15e9fdadbba277f29a89b87a77dd6eb83bd12aa60bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2015-12-16T09:09:01Z",
    "title_canon_sha256": "82d81abeb7430357a21ad9e73f18efe5c4742b9ccbdb5f5a42f3fa8bfc56a11d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05095",
    "kind": "arxiv",
    "version": 1
  }
}