Pith Number

pith:PBPNDJUQ

pith:2021:PBPNDJUQ6M3VMBJJ3ZBPVZPSYG

not attested not anchored not stored refs pending

Bohmian Trajectories of the Time-oscillating Schr\"odinger Equations

Ao Zhang, Dandan Li, Jinqiao Duan, Li Lin

arxiv:2109.04039 v1 · 2021-09-09 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PBPNDJUQ6M3VMBJJ3ZBPVZPSYG}

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	2026-07-05T08:33:22.877119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

785ed1a690f337560529de42fae5f2c19703cc77c8be458d7cb10b103875ceef

Aliases

arxiv: 2109.04039 · arxiv_version: 2109.04039v1 · doi: 10.48550/arxiv.2109.04039 · pith_short_12: PBPNDJUQ6M3V · pith_short_16: PBPNDJUQ6M3VMBJJ · pith_short_8: PBPNDJUQ

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/PBPNDJUQ6M3VMBJJ3ZBPVZPSYG \
  | 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: 785ed1a690f337560529de42fae5f2c19703cc77c8be458d7cb10b103875ceef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4817b6f741677af10a7f5b4d19da7d5c404b9c6b8ec4fc8400e0256503e7d06f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2021-09-09T05:16:02Z",
    "title_canon_sha256": "930b80713ef5b92f1f0eac979444fac25991050187908c2fc0dec56d0ce9ac3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.04039",
    "kind": "arxiv",
    "version": 1
  }
}