Pith Number

pith:PMIGRF4D

pith:2020:PMIGRF4DRQQMHIBGJSCS7Z6KVC

not attested not anchored not stored refs pending

Homotopy motions of surfaces in $3$-manifolds

Makoto Sakuma, Yuya Koda

arxiv:2011.05766 v4 · 2020-11-11 · 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{PMIGRF4DRQQMHIBGJSCS7Z6KVC}

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	2026-07-05T04:28:25.827138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b106897838c20c3a0264c852fe7caa884d88033635976495559492e164de26e

Aliases

arxiv: 2011.05766 · arxiv_version: 2011.05766v4 · doi: 10.48550/arxiv.2011.05766 · pith_short_12: PMIGRF4DRQQM · pith_short_16: PMIGRF4DRQQMHIBG · pith_short_8: PMIGRF4D

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/PMIGRF4DRQQMHIBGJSCS7Z6KVC \
  | 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: 7b106897838c20c3a0264c852fe7caa884d88033635976495559492e164de26e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "473c0ee013172197de06c9d3531f9bc1df38ef701e293c7f0e11c4ad079ab63a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-11-11T13:22:36Z",
    "title_canon_sha256": "61feb7f7c7d64613005214187d389e37b9844f50d59f838fcd042dc1f12acb17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.05766",
    "kind": "arxiv",
    "version": 4
  }
}