Pith Number

pith:B7TIVCXH

pith:2020:B7TIVCXHOWGQOJ72F7HWWAWVOH

not attested not anchored not stored refs pending

Hamilton type entropy formula along the Ricci flow on surfaces with boundary

Keita Kunikawa, Yohei Sakurai

arxiv:2010.09179 v2 · 2020-10-19 · 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{B7TIVCXHOWGQOJ72F7HWWAWVOH}

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	2026-07-05T02:55:53.066657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fe68a8ae7758d0727fa2fcf6b02d571c9e9b48c244ee2b918d67fbbeb300761

Aliases

arxiv: 2010.09179 · arxiv_version: 2010.09179v2 · doi: 10.48550/arxiv.2010.09179 · pith_short_12: B7TIVCXHOWGQ · pith_short_16: B7TIVCXHOWGQOJ72 · pith_short_8: B7TIVCXH

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/B7TIVCXHOWGQOJ72F7HWWAWVOH \
  | 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: 0fe68a8ae7758d0727fa2fcf6b02d571c9e9b48c244ee2b918d67fbbeb300761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a22de9df97800e3836c03772df3b0479ae03e0af672cb69d3e89c1b063f58c74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-10-19T03:03:15Z",
    "title_canon_sha256": "1d4e6c6e3a6b492322c8ae2ce21cdc35a200b9b7a28cf08d7e792cf582755087"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.09179",
    "kind": "arxiv",
    "version": 2
  }
}