Pith Number

pith:2KWMI2RD

pith:2014:2KWMI2RD7X54BP3IKPIRMGK4WH

not attested not anchored not stored refs pending

Tangent spaces and tangent bundles for diffeological spaces

Enxin Wu, J. Daniel Christensen

arxiv:1411.5425 v3 · 2014-11-20 · 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{2KWMI2RD7X54BP3IKPIRMGK4WH}

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

1 paper in Pith

Higher Order Automatic Differentiation of Higher Order Functions

Receipt and verification

First computed	2026-05-18T00:40:42.014918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c

Aliases

arxiv: 1411.5425 · arxiv_version: 1411.5425v3 · doi: 10.48550/arxiv.1411.5425 · pith_short_12: 2KWMI2RD7X54 · pith_short_16: 2KWMI2RD7X54BP3I · pith_short_8: 2KWMI2RD

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/2KWMI2RD7X54BP3IKPIRMGK4WH \
  | 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: d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "804f72f42eb3b8684c5be43d5ed9a6313e33aa694ed8e6360df83685d9f2b852",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-11-20T02:39:55Z",
    "title_canon_sha256": "70fabe8897e31511ae1757d5ac18601c0ff517411325db255c1aac5b36f10c3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.5425",
    "kind": "arxiv",
    "version": 3
  }
}