{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GKTRY4CGB6QSWWT6K273MKE5TH","short_pith_number":"pith:GKTRY4CG","canonical_record":{"source":{"id":"1508.01874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2015-08-08T09:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"5930d34ebb510a496b1a7f5935398e986a5f75b997341a87030e4185694f3663","abstract_canon_sha256":"892576ca473b2c312b4a9c73c00be4b63e2d280e102e1723831115bfd12c20ba"},"schema_version":"1.0"},"canonical_sha256":"32a71c70460fa12b5a7e56bfb6289d99c76963e982cd7d838dbf4237ec375223","source":{"kind":"arxiv","id":"1508.01874","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01874","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01874v1","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01874","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"GKTRY4CGB6QS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GKTRY4CGB6QSWWT6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GKTRY4CG","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GKTRY4CGB6QSWWT6K273MKE5TH","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2015-08-08T09:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"5930d34ebb510a496b1a7f5935398e986a5f75b997341a87030e4185694f3663","abstract_canon_sha256":"892576ca473b2c312b4a9c73c00be4b63e2d280e102e1723831115bfd12c20ba"},"schema_version":"1.0"},"canonical_sha256":"32a71c70460fa12b5a7e56bfb6289d99c76963e982cd7d838dbf4237ec375223","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:28.203548Z","signature_b64":"fK2QRL230B7aennnSqT1LYoj8aLqfinN9IWY/DexOriD6fRMaYJgvpfIGghdNbA5W5XO6RNYAEDO2lkbPCMgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a71c70460fa12b5a7e56bfb6289d99c76963e982cd7d838dbf4237ec375223","last_reissued_at":"2026-05-18T01:32:28.202465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:28.202465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01874","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRvYHGrk+Xoc6f96tcHrI1NdStwvwyoXujbOKqoilOhU+SiMor/6B8hoaj5/86VtUl7EIyKHhVFdF/xon2inCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:15:03.556709Z"},"content_sha256":"b0a4e6b28509625437eab3dd2c95747527a858c08ad5010d77920cc657fc006c","schema_version":"1.0","event_id":"sha256:b0a4e6b28509625437eab3dd2c95747527a858c08ad5010d77920cc657fc006c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GKTRY4CGB6QSWWT6K273MKE5TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of galaxies gravitational field stemming from their tidal interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Vladimir Stephanovich, Wlodzimierz Godlowski","submitted_at":"2015-08-08T09:17:50Z","abstract_excerpt":"We calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal in- teraction. For that we apply the statistical method of Chandrasekhar (1943), used there to calculate famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01874","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAVLTUUz5prTvA8fekTblniBU0fU6CwMTh2zCOGH8ecueuuxyUDa5socW3bQpfxprY7kXe0kVl+Nzzh6VgD/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:15:03.557408Z"},"content_sha256":"845810e9e7de88e5be938df966a8ec2c0b1af02d90aa302ecad8c979395547f1","schema_version":"1.0","event_id":"sha256:845810e9e7de88e5be938df966a8ec2c0b1af02d90aa302ecad8c979395547f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKTRY4CGB6QSWWT6K273MKE5TH/bundle.json","state_url":"https://pith.science/pith/GKTRY4CGB6QSWWT6K273MKE5TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKTRY4CGB6QSWWT6K273MKE5TH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T20:15:03Z","links":{"resolver":"https://pith.science/pith/GKTRY4CGB6QSWWT6K273MKE5TH","bundle":"https://pith.science/pith/GKTRY4CGB6QSWWT6K273MKE5TH/bundle.json","state":"https://pith.science/pith/GKTRY4CGB6QSWWT6K273MKE5TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKTRY4CGB6QSWWT6K273MKE5TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GKTRY4CGB6QSWWT6K273MKE5TH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"892576ca473b2c312b4a9c73c00be4b63e2d280e102e1723831115bfd12c20ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2015-08-08T09:17:50Z","title_canon_sha256":"5930d34ebb510a496b1a7f5935398e986a5f75b997341a87030e4185694f3663"},"schema_version":"1.0","source":{"id":"1508.01874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01874","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01874v1","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01874","created_at":"2026-05-18T01:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"GKTRY4CGB6QS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GKTRY4CGB6QSWWT6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GKTRY4CG","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:845810e9e7de88e5be938df966a8ec2c0b1af02d90aa302ecad8c979395547f1","target":"graph","created_at":"2026-05-18T01:32:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal in- teraction. For that we apply the statistical method of Chandrasekhar (1943), used there to calculate famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we","authors_text":"Vladimir Stephanovich, Wlodzimierz Godlowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2015-08-08T09:17:50Z","title":"The distribution of galaxies gravitational field stemming from their tidal interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01874","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b0a4e6b28509625437eab3dd2c95747527a858c08ad5010d77920cc657fc006c","target":"record","created_at":"2026-05-18T01:32:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"892576ca473b2c312b4a9c73c00be4b63e2d280e102e1723831115bfd12c20ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2015-08-08T09:17:50Z","title_canon_sha256":"5930d34ebb510a496b1a7f5935398e986a5f75b997341a87030e4185694f3663"},"schema_version":"1.0","source":{"id":"1508.01874","kind":"arxiv","version":1}},"canonical_sha256":"32a71c70460fa12b5a7e56bfb6289d99c76963e982cd7d838dbf4237ec375223","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a71c70460fa12b5a7e56bfb6289d99c76963e982cd7d838dbf4237ec375223","first_computed_at":"2026-05-18T01:32:28.202465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:28.202465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fK2QRL230B7aennnSqT1LYoj8aLqfinN9IWY/DexOriD6fRMaYJgvpfIGghdNbA5W5XO6RNYAEDO2lkbPCMgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:28.203548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0a4e6b28509625437eab3dd2c95747527a858c08ad5010d77920cc657fc006c","sha256:845810e9e7de88e5be938df966a8ec2c0b1af02d90aa302ecad8c979395547f1"],"state_sha256":"62ce985a9628b46df749eadc1ea4401da7b335fb2e323c619977045a8f6bed21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZfbXjVUT1OAmv4SxjWQnb/XQ8eVKaUFO9E6wR890i2dnCzD5imo/XBl5qlU+CTmUCFxqAMSRrpTG+r8PmhbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:15:03.560918Z","bundle_sha256":"5e33cef8e4ef29f9fdb46417ab97e06c730de0befe5e392afde371f317936a7c"}}