Pith Number

pith:KNNGUSA2

pith:2010:KNNGUSA2GGTTK6W6HJMKGGKDNA

not attested not anchored not stored refs pending

Negative mode of Schwarzschild black hole from the thermodynamic instability

Takayuki Hirayama

arxiv:1012.0441 v2 · 2010-12-02 · hep-th · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KNNGUSA2GGTTK6W6HJMKGGKDNA}

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	2026-05-18T04:13:16.012060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535a6a481a31a7357ade3a58a31943681d6f1c49d9aedd731c208006ae75a7b3

Aliases

arxiv: 1012.0441 · arxiv_version: 1012.0441v2 · doi: 10.48550/arxiv.1012.0441 · pith_short_12: KNNGUSA2GGTT · pith_short_16: KNNGUSA2GGTTK6W6 · pith_short_8: KNNGUSA2

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/KNNGUSA2GGTTK6W6HJMKGGKDNA \
  | 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: 535a6a481a31a7357ade3a58a31943681d6f1c49d9aedd731c208006ae75a7b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6675977a1edbb71d270df5150078bb17ac5aafa2e996f9a72e0d4be11498202",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2010-12-02T14:55:27Z",
    "title_canon_sha256": "9f3572bcc19d15b7acc8cc11d21ee483d1c36df1e6e8f212681f03416f9f9816"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0441",
    "kind": "arxiv",
    "version": 2
  }
}