Pith Number

pith:H5K2C6HZ

pith:2009:H5K2C6HZ4MI4XWVPO5GA3UE62M

not attested not anchored not stored refs pending

PT symmetry as a necessary and sufficient condition for unitary time evolution

Philip D. Mannheim

arxiv:0912.2635 v3 · 2009-12-14 · 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{H5K2C6HZ4MI4XWVPO5GA3UE62M}

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	2026-05-18T03:40:03.787882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f55a178f9e311cbdaaf774c0dd09ed31974feb7b8752fd4016f57ecafbf9978

Aliases

arxiv: 0912.2635 · arxiv_version: 0912.2635v3 · doi: 10.48550/arxiv.0912.2635 · pith_short_12: H5K2C6HZ4MI4 · pith_short_16: H5K2C6HZ4MI4XWVP · pith_short_8: H5K2C6HZ

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/H5K2C6HZ4MI4XWVPO5GA3UE62M \
  | 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: 3f55a178f9e311cbdaaf774c0dd09ed31974feb7b8752fd4016f57ecafbf9978

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27519a2a4528f5c0eaf1fbe713239b45b9bd83f01317d1ebcb02e6e4b62a321d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2009-12-14T12:56:06Z",
    "title_canon_sha256": "a82ea8526a9f0fba0469459b17ac2921fb19af5410b02924bf20eb672e79a808"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2635",
    "kind": "arxiv",
    "version": 3
  }
}