{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:M3YTZ7OP74K7O6PYSYVTZY5ZBV","short_pith_number":"pith:M3YTZ7OP","canonical_record":{"source":{"id":"1312.7790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-30T17:32:28Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"708db90a2ee9882ab7fd0fb98bf67ff94a87a83dab2f8b56c7a0d64e50a76836","abstract_canon_sha256":"1f90faf2c71cc14b1398c293532e2280620b12b08db1f1e2d8f8181dd51b2967"},"schema_version":"1.0"},"canonical_sha256":"66f13cfdcfff15f779f8962b3ce3b90d5b86406c9efdddcb51c60c111f77cc1a","source":{"kind":"arxiv","id":"1312.7790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7790","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7790v1","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7790","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"M3YTZ7OP74K7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M3YTZ7OP74K7O6PY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M3YTZ7OP","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:M3YTZ7OP74K7O6PYSYVTZY5ZBV","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-30T17:32:28Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"708db90a2ee9882ab7fd0fb98bf67ff94a87a83dab2f8b56c7a0d64e50a76836","abstract_canon_sha256":"1f90faf2c71cc14b1398c293532e2280620b12b08db1f1e2d8f8181dd51b2967"},"schema_version":"1.0"},"canonical_sha256":"66f13cfdcfff15f779f8962b3ce3b90d5b86406c9efdddcb51c60c111f77cc1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:51.132616Z","signature_b64":"ySmvdH48zh4rVtDEdCgas7fT1UOPKe2laawhToB3ZCXhtb6WdR5TIDIEoFUvvyVZPn6mDQKnXRiz2yGVju8tBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66f13cfdcfff15f779f8962b3ce3b90d5b86406c9efdddcb51c60c111f77cc1a","last_reissued_at":"2026-05-18T03:00:51.132164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:51.132164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7790","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":"2026-05-18T03:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLo3Ihz9lXG4TS5zq3bta/RuRFFVHwP8OFNyrP51rIWoQJ/xvgfs4j9PyrehM/oYs4Eq2kn3WUJylzCr2t6pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:19:03.435880Z"},"content_sha256":"a8521dae32391f6cf25e8397a73ecec21cc00a1d76c68d24ee8e54b1504fb23c","schema_version":"1.0","event_id":"sha256:a8521dae32391f6cf25e8397a73ecec21cc00a1d76c68d24ee8e54b1504fb23c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:M3YTZ7OP74K7O6PYSYVTZY5ZBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comments on \"Growth of Covariant Perturbations in the Contracting Phase of a Bouncing Universe\" by A. Kumar","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"N. Pinto-Neto, S. D. P. Vitenti","submitted_at":"2013-12-30T17:32:28Z","abstract_excerpt":"A recent paper by Kumar (2012) (hereafter K12) claimed that in a contracting model, described by perturbations around a collapsing Friedmann model containing dust or radiation, the perturbations can grow in such a way that the linearity conditions would become invalid. This conclusion is not correct due to the following facts: first, it is claimed that the linearity conditions are not satisfied, but nowhere in K12 the amplitudes of the perturbations were in fact estimated. Therefore, without such estimates, the only possible conclusion from this work is the well known fact that the perturbatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7790","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":"2026-05-18T03:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wS3TA0fcN3/dxV4FGuhlvuCu6jqVN29Mx3Kn0tYnlVPrrD6d2C1L61UfH8E2EUyX0Ywpps9HYHc1sbvwDXvgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:19:03.436565Z"},"content_sha256":"39d89032334630580708d2162b0e535deb7afbc09b887e37d0e79a937a963d09","schema_version":"1.0","event_id":"sha256:39d89032334630580708d2162b0e535deb7afbc09b887e37d0e79a937a963d09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/bundle.json","state_url":"https://pith.science/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/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":"2026-05-26T23:19:03Z","links":{"resolver":"https://pith.science/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV","bundle":"https://pith.science/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/bundle.json","state":"https://pith.science/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3YTZ7OP74K7O6PYSYVTZY5ZBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M3YTZ7OP74K7O6PYSYVTZY5ZBV","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":"1f90faf2c71cc14b1398c293532e2280620b12b08db1f1e2d8f8181dd51b2967","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-30T17:32:28Z","title_canon_sha256":"708db90a2ee9882ab7fd0fb98bf67ff94a87a83dab2f8b56c7a0d64e50a76836"},"schema_version":"1.0","source":{"id":"1312.7790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7790","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7790v1","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7790","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"M3YTZ7OP74K7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M3YTZ7OP74K7O6PY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M3YTZ7OP","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:39d89032334630580708d2162b0e535deb7afbc09b887e37d0e79a937a963d09","target":"graph","created_at":"2026-05-18T03:00:51Z","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":"A recent paper by Kumar (2012) (hereafter K12) claimed that in a contracting model, described by perturbations around a collapsing Friedmann model containing dust or radiation, the perturbations can grow in such a way that the linearity conditions would become invalid. This conclusion is not correct due to the following facts: first, it is claimed that the linearity conditions are not satisfied, but nowhere in K12 the amplitudes of the perturbations were in fact estimated. Therefore, without such estimates, the only possible conclusion from this work is the well known fact that the perturbatio","authors_text":"N. Pinto-Neto, S. D. P. Vitenti","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-30T17:32:28Z","title":"Comments on \"Growth of Covariant Perturbations in the Contracting Phase of a Bouncing Universe\" by A. Kumar"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7790","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:a8521dae32391f6cf25e8397a73ecec21cc00a1d76c68d24ee8e54b1504fb23c","target":"record","created_at":"2026-05-18T03:00:51Z","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":"1f90faf2c71cc14b1398c293532e2280620b12b08db1f1e2d8f8181dd51b2967","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-30T17:32:28Z","title_canon_sha256":"708db90a2ee9882ab7fd0fb98bf67ff94a87a83dab2f8b56c7a0d64e50a76836"},"schema_version":"1.0","source":{"id":"1312.7790","kind":"arxiv","version":1}},"canonical_sha256":"66f13cfdcfff15f779f8962b3ce3b90d5b86406c9efdddcb51c60c111f77cc1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66f13cfdcfff15f779f8962b3ce3b90d5b86406c9efdddcb51c60c111f77cc1a","first_computed_at":"2026-05-18T03:00:51.132164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:51.132164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ySmvdH48zh4rVtDEdCgas7fT1UOPKe2laawhToB3ZCXhtb6WdR5TIDIEoFUvvyVZPn6mDQKnXRiz2yGVju8tBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:51.132616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8521dae32391f6cf25e8397a73ecec21cc00a1d76c68d24ee8e54b1504fb23c","sha256:39d89032334630580708d2162b0e535deb7afbc09b887e37d0e79a937a963d09"],"state_sha256":"5ad72b494c803d81110f4320a9c6d4bc5ca570aea0f779a9bf4bfb0e28ab001e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TQmn8Nuh46Emt8rV/kWkHQ9+hD32odEblNvw1qA+sscBeYs47Bvkwxze9qWco994bI/suzs+P51F9iMw9NmdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:19:03.439979Z","bundle_sha256":"c69ff85129bfbfb9ac1016990c449c48198f08e01c2acaafd0d989aebddbe771"}}