Pith Number

pith:SFERDY52

pith:2021:SFERDY523LHJZD33VVUK56GWGR

not attested not anchored not stored refs pending

Topology of spaces of smooth functions and gradient-like flows with prescribed singularities on surfaces

Elena A. Kudryavtseva

arxiv:2106.03017 v1 · 2021-06-06 · math.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SFERDY523LHJZD33VVUK56GWGR}

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

Smooth functions that split a Klein bottle into two M\"obius bands

Receipt and verification

First computed	2026-07-05T02:46:32.779692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

914911e3badace9c8f7bad68aef8d634511dd1abc39f20cb2f1e5055ef49446f

Aliases

arxiv: 2106.03017 · arxiv_version: 2106.03017v1 · doi: 10.48550/arxiv.2106.03017 · pith_short_12: SFERDY523LHJ · pith_short_16: SFERDY523LHJZD33 · pith_short_8: SFERDY52

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/SFERDY523LHJZD33VVUK56GWGR \
  | 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: 914911e3badace9c8f7bad68aef8d634511dd1abc39f20cb2f1e5055ef49446f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee1e55a0df77d349310d84420d5a68817186d97d4dd515b495272b7538e09de0",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-06-06T03:09:12Z",
    "title_canon_sha256": "09a137f5d10d7fb6742e81db4db03a1d756b6848d9a0634955cf63dbd7c055b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.03017",
    "kind": "arxiv",
    "version": 1
  }
}