Pith Number

pith:YGH472I6

pith:2021:YGH472I6TWDSCUR7BC3FMGOVUB

not attested not anchored not stored refs pending

Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry

Keita Kunikawa, Yohei Sakurai

arxiv:2104.05191 v2 · 2021-04-12 · 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{YGH472I6TWDSCUR7BC3FMGOVUB}

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	2026-07-05T03:02:50.404725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c18fcfe91e9d8721523f08b65619d5a042c9d459a3573e3947014cc55af95507

Aliases

arxiv: 2104.05191 · arxiv_version: 2104.05191v2 · doi: 10.48550/arxiv.2104.05191 · pith_short_12: YGH472I6TWDS · pith_short_16: YGH472I6TWDSCUR7 · pith_short_8: YGH472I6

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/YGH472I6TWDSCUR7BC3FMGOVUB \
  | 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: c18fcfe91e9d8721523f08b65619d5a042c9d459a3573e3947014cc55af95507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18b97fb6203047992a623e2a7a0cd02d9da66b78a2a5c0680fb395a2ea7a766a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-04-12T04:05:18Z",
    "title_canon_sha256": "33df4bd476d0666839f6d66d02a8c2fb257dc38014bd945d6f30b63d0ee6dd1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.05191",
    "kind": "arxiv",
    "version": 2
  }
}