Timestamp proof

This problem was hashed with SHA-256 and the digest was committed to the Bitcoin blockchain through OpenTimestamps. The proof shows the exact text below existed no later than the anchoring block. Only the digest ever left PubPhys.

Status
Anchored in Bitcoin
Bitcoin block
#969,239
Block time
2026-09-30 02:33 UTC
Recorded
2026-09-30 01:04 UTC
SHA-256
5ef69442170ee3a68c0df6f6c3583ef9724f85b26c98fcb006606819c4e688cf

Verify it

1. Here, in one click

Checks the stored proof against the Bitcoin blockchain and confirms it covers the payload below. To check files you downloaded, use Verify a timestamp.

2. On opentimestamps.org (independent of PubPhys)

  1. Download the payload (.json) and the proof (.ots) above.
  2. Open opentimestamps.org and drop pubphys-problem-41-stamp-9.json.ots onto Drop here a file to stamp or an .ots proof file to verify in the Stamp & Verify section.
  3. Then drop pubphys-problem-41-stamp-9.json onto Drop here the stamped file.
  4. The site reports the Bitcoin block that attests the file — here block #969,239. Your file never leaves the browser; only its hash is compared.

3. From the command line

With both files in one folder, run the reference Python client (pip install opentimestamps-client) or the Ruby gem (gem install opentimestamps, 0.4 or newer):

ots verify pubphys-problem-41-stamp-9.json.ots

The Ruby gem checks the block against a public block explorer. The Python client checks it only against your own Bitcoin Core node; without one, run ots --no-bitcoin verify pubphys-problem-41-stamp-9.json.ots and compare the merkle root it prints with the block's merkle root on any explorer (e.g. block 969239).

Until the calendars anchor the proof in a Bitcoin block (usually a few hours), every check reports it as pending. Once PubPhys shows a block number, download the proof again, or complete your copy with ots upgrade pubphys-problem-41-stamp-9.json.ots.

Hashed payload

{
  "author": "grigori_p",
  "field": "gravitation",
  "id": 41,
  "published_at": "2026-07-05T05:48:51Z",
  "recorded_at": "2026-09-30T01:04:42Z",
  "references": null,
  "schema": "physicdb.problem/1",
  "site": "physicdb.yet.bz",
  "slug": "the-black-hole-information-paradox",
  "statement": "Hawking radiation appears thermal, with temperature\n$$T_H = \\frac{\\hbar c^3}{8\\pi G M k_B},$$\nsuggesting that a black hole formed from a pure state evaporates into a mixed state — violating unitarity.\n\nHow is quantum information preserved (or not) during black hole evaporation? Recent island/replica-wormhole computations reproduce a unitary Page curve, but the mechanism of information return is not fully understood.\n",
  "title": "The Black Hole Information Paradox"
}

Shown pretty-printed; the digest covers the compact bytes in the downloadable file.