Pith Number

pith:3MVKEPPT

pith:2014:3MVKEPPTJOVNV2QXOXXTQWQL2A

not attested not anchored not stored refs pending

Cut and conjugate points of the exponential map, with applications

Pablo Angulo Ardoy

arxiv:1411.3933 v1 · 2014-11-14 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3MVKEPPTJOVNV2QXOXXTQWQL2A}

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	2026-05-18T02:37:37.332695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418

Aliases

arxiv: 1411.3933 · arxiv_version: 1411.3933v1 · doi: 10.48550/arxiv.1411.3933 · pith_short_12: 3MVKEPPTJOVN · pith_short_16: 3MVKEPPTJOVNV2QX · pith_short_8: 3MVKEPPT

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/3MVKEPPTJOVNV2QXOXXTQWQL2A \
  | 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: db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb7a7c4cf1cc92cc73eefa826d2d465a60e536ae0b2aa2bf9f12a445adc7303f",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-11-14T15:16:53Z",
    "title_canon_sha256": "01886209fa13daeb477c7ea3275bb16e8a695b3863bafe6aa36e988dc3c1acdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.3933",
    "kind": "arxiv",
    "version": 1
  }
}