Pith Number

pith:YNPZ3OPU

pith:2016:YNPZ3OPUW4DOT7KTQFQDGUSLEQ

not attested not anchored not stored refs pending

Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric

Fran\c{c}ois-Xavier Vialard (Ceremade, Mokaplan), Rabah Tahraoui

arxiv:1606.04230 v2 · 2016-06-14 · 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{YNPZ3OPUW4DOT7KTQFQDGUSLEQ}

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	2026-05-18T01:05:12.213635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c35f9db9f4b706e9fd53816033524b241c51074a5efb36fb8a68663b7cf8cf5a

Aliases

arxiv: 1606.04230 · arxiv_version: 1606.04230v2 · doi: 10.48550/arxiv.1606.04230 · pith_short_12: YNPZ3OPUW4DO · pith_short_16: YNPZ3OPUW4DOT7KT · pith_short_8: YNPZ3OPU

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/YNPZ3OPUW4DOT7KTQFQDGUSLEQ \
  | 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: c35f9db9f4b706e9fd53816033524b241c51074a5efb36fb8a68663b7cf8cf5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baa2f1f7ab6e249983975b24834b074673631bee1d4378b41281ec0cab66fdc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-06-14T07:31:10Z",
    "title_canon_sha256": "f4fdc5f4cb1d5e811f7709694a07c09fb0ff8ec2d323042ad4e586709be85835"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04230",
    "kind": "arxiv",
    "version": 2
  }
}