Pith Number

pith:NUJBDKFJ

pith:2011:NUJBDKFJRW3BLO7WIVODSH3VSR

not attested not anchored not stored refs pending

Homotopy Groups, Focal Points and Totally Geodesic Immersions

Heudson Mirandola, S\'ergio Mendon\c{c}a

arxiv:1108.1822 v2 · 2011-08-08 · 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{NUJBDKFJRW3BLO7WIVODSH3VSR}

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	2026-05-18T03:22:06.433973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d1211a8a98db615bbf6455c391f759440fbd7495c0a8527e06cc9a7b2f59ce9

Aliases

arxiv: 1108.1822 · arxiv_version: 1108.1822v2 · doi: 10.48550/arxiv.1108.1822 · pith_short_12: NUJBDKFJRW3B · pith_short_16: NUJBDKFJRW3BLO7W · pith_short_8: NUJBDKFJ

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/NUJBDKFJRW3BLO7WIVODSH3VSR \
  | 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: 6d1211a8a98db615bbf6455c391f759440fbd7495c0a8527e06cc9a7b2f59ce9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a887fec3f24a43b2e9864e637a953e2835f6e39999097c09b34d6219597f95cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-08T22:23:21Z",
    "title_canon_sha256": "431b4da447cfb230627f975006366f41552cfd0e5b2272bcc6164751729126a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1822",
    "kind": "arxiv",
    "version": 2
  }
}