Pith Number

pith:G6VOVIXH

pith:2021:G6VOVIXHPC3OIHIARJ32U6MZCW

not attested not anchored not stored refs pending

Defect $a$-Theorem and $a$-Maximization

Yifan Wang

arxiv:2101.12648 v1 · 2021-01-29 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G6VOVIXHPC3OIHIARJ32U6MZCW}

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	2026-07-05T03:58:46.202175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37aaeaa2e778b6e41d008a77aa7999159bd4c29b3b1ea2f70e5ce7be11ae51fe

Aliases

arxiv: 2101.12648 · arxiv_version: 2101.12648v1 · doi: 10.48550/arxiv.2101.12648 · pith_short_12: G6VOVIXHPC3O · pith_short_16: G6VOVIXHPC3OIHIA · pith_short_8: G6VOVIXH

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/G6VOVIXHPC3OIHIARJ32U6MZCW \
  | 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: 37aaeaa2e778b6e41d008a77aa7999159bd4c29b3b1ea2f70e5ce7be11ae51fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7138c5ca305c7114eca9b290f9879a4b9bb3160b72ad5889c629dd6719971e02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2021-01-29T15:40:12Z",
    "title_canon_sha256": "cd434ba90b5bea1525d6b9a28e6df2ab5c062243229c2403937df9926553856b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.12648",
    "kind": "arxiv",
    "version": 1
  }
}