Pith Number

pith:CYJODDZ4

pith:2010:CYJODDZ4SQDYB7F7WET2V7NK5X

not attested not anchored not stored refs pending

Invariants of singular sets of smooth maps

Rustam Sadykov

arxiv:1004.0460 v1 · 2010-04-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CYJODDZ4SQDYB7F7WET2V7NK5X}

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	2026-05-18T02:24:17.782200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1612e18f3c940780fcbfb127aafdaaedfc89ec985038331e836b5dd736bf5b0f

Aliases

arxiv: 1004.0460 · arxiv_version: 1004.0460v1 · doi: 10.48550/arxiv.1004.0460 · pith_short_12: CYJODDZ4SQDY · pith_short_16: CYJODDZ4SQDYB7F7 · pith_short_8: CYJODDZ4

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/CYJODDZ4SQDYB7F7WET2V7NK5X \
  | 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: 1612e18f3c940780fcbfb127aafdaaedfc89ec985038331e836b5dd736bf5b0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65fbc150bb3caadd6a8b3ce3ac7142fa0be13b3e505b9b740dd8df2996992198",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-04-03T18:41:36Z",
    "title_canon_sha256": "2dace08463efa0f15fc513e0551cc71385731686f8426513672d1a0c90e152ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0460",
    "kind": "arxiv",
    "version": 1
  }
}