Pith Number

pith:XQNMIXR2

pith:2018:XQNMIXR2AJTXDROBMMNNVXU45L

not attested not anchored not stored refs pending

Critical points and surjectivity of smooth maps

Chengjie Yu, Yongjie Shi

arxiv:1804.10853 v1 · 2018-04-28 · math.CA · 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{XQNMIXR2AJTXDROBMMNNVXU45L}

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	2026-05-18T00:17:15.331801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc1ac45e3a026771c5c1631adade9ceae22369380fc276c693d6567d804c046a

Aliases

arxiv: 1804.10853 · arxiv_version: 1804.10853v1 · doi: 10.48550/arxiv.1804.10853 · pith_short_12: XQNMIXR2AJTX · pith_short_16: XQNMIXR2AJTXDROB · pith_short_8: XQNMIXR2

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/XQNMIXR2AJTXDROBMMNNVXU45L \
  | 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: bc1ac45e3a026771c5c1631adade9ceae22369380fc276c693d6567d804c046a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f22a9cc6547d16c8c015f3c8691ed226b905674cc6e8919e954a943e58be3b5",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-04-28T23:02:22Z",
    "title_canon_sha256": "b551162e33f847379143201ede2007c67614176f3266b3ad01a7b4bb4c9edbe6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.10853",
    "kind": "arxiv",
    "version": 1
  }
}