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
- d25a0adb90f5d1d9931d51dbff6c878235b2bbb8a2d9b5e6113602a8f6b84b0b
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)
- Download the payload (.json) and the proof (.ots) above.
- Open opentimestamps.org and drop pubphys-problem-47-stamp-15.json.ots onto Drop here a file to stamp or an .ots proof file to verify in the Stamp & Verify section.
- Then drop pubphys-problem-47-stamp-15.json onto Drop here the stamped file.
- 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-47-stamp-15.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-47-stamp-15.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-47-stamp-15.json.ots.
Hashed payload
{
"author": "grigori_p",
"field": "statistical_mechanics",
"id": 47,
"published_at": "2026-07-28T05:48:51Z",
"recorded_at": "2026-09-30T01:04:42Z",
"references": null,
"schema": "physicdb.problem/1",
"site": "physicdb.yet.bz",
"slug": "the-arrow-of-time-and-the-low-entropy-past",
"statement": "The microscopic laws are (nearly) time-symmetric, yet entropy increases,\n$$\\frac{dS}{dt} \\geq 0.$$\nThis macroscopic arrow is usually traced to an extraordinarily low-entropy initial state of the universe (the \"Past Hypothesis\").\n\nWhy did the early universe have such low entropy, and can the thermodynamic arrow be derived without simply postulating it?\n",
"title": "The Arrow of Time and the Low-Entropy Past"
}
Shown pretty-printed; the digest covers the compact bytes in the downloadable file.