Pith Number

pith:IAVLOUT3

pith:2021:IAVLOUT3KMYMQVDUSYQUFCTNFB

not attested not anchored not stored refs pending

Deflection and gravitational lensing of null and timelike signals in general asymptotically (anti-)de Sitter spacetimes

Haotian Liu, Junji Jia, Zixiao Li

arxiv:2107.11616 v1 · 2021-07-24 · 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{IAVLOUT3KMYMQVDUSYQUFCTNFB}

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	2026-07-05T03:21:56.472296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

402ab7527b5330c854749621428a6d286bd914cf876b07cfa57798eb25d74615

Aliases

arxiv: 2107.11616 · arxiv_version: 2107.11616v1 · doi: 10.48550/arxiv.2107.11616 · pith_short_12: IAVLOUT3KMYM · pith_short_16: IAVLOUT3KMYMQVDU · pith_short_8: IAVLOUT3

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/IAVLOUT3KMYMQVDUSYQUFCTNFB \
  | 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: 402ab7527b5330c854749621428a6d286bd914cf876b07cfa57798eb25d74615

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b64191f94e988244a5b2fa682cb8689d290d3ad9f61aba4e066194bedec1516b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-07-24T14:11:09Z",
    "title_canon_sha256": "aefa374250193983ab665ffc07ffd22c2c114ff94e505dc6df8a18e31b453f0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.11616",
    "kind": "arxiv",
    "version": 1
  }
}