Pith Number

pith:Z7BWJU26

pith:2021:Z7BWJU26WLK74HQ2I3RLW7DO47

not attested not anchored not stored refs pending

Hidden conformal symmetry on the black hole photon sphere

Bernard Raffaelli

arxiv:2112.12543 v1 · 2021-12-23 · 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{Z7BWJU26WLK74HQ2I3RLW7DO47}

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.

Cited by

1 paper in Pith

Black Hole Photon Rings Saturate the Quantum Chaos Bound

Receipt and verification

First computed	2026-07-05T04:07:43.253367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfc364d35eb2d5fe1e1a46e2bb7c6ee7f38e799b9d191fe7120e9d0ae1806b05

Aliases

arxiv: 2112.12543 · arxiv_version: 2112.12543v1 · doi: 10.48550/arxiv.2112.12543 · pith_short_12: Z7BWJU26WLK7 · pith_short_16: Z7BWJU26WLK74HQ2 · pith_short_8: Z7BWJU26

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/Z7BWJU26WLK74HQ2I3RLW7DO47 \
  | 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: cfc364d35eb2d5fe1e1a46e2bb7c6ee7f38e799b9d191fe7120e9d0ae1806b05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6066d79455918ab4e8ee12554c0eeb49798be9961ece5ca6e241d8b9bb31a72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-12-23T13:57:03Z",
    "title_canon_sha256": "0cb42e6050bb38a973281039b334fe254e74c9e9868a87c84820daaae1e4b1f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.12543",
    "kind": "arxiv",
    "version": 1
  }
}