{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3CPN2C4VPXBDPD5TGXAOQXOIR7","short_pith_number":"pith:3CPN2C4V","canonical_record":{"source":{"id":"1612.00974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-03T15:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"a5eb1cca27302fe3ba494a403be37a96b6385e88e8132fa9faf5a2abf96b0603","abstract_canon_sha256":"d157463342d1198adfcd05c2eb1095a93023e724ddedbab088c9c2e2e9b1aefe"},"schema_version":"1.0"},"canonical_sha256":"d89edd0b957dc2378fb335c0e85dc88fe73cbd6996a969667ab3965066c41fee","source":{"kind":"arxiv","id":"1612.00974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00974","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00974v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00974","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"3CPN2C4VPXBD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3CPN2C4VPXBDPD5T","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3CPN2C4V","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3CPN2C4VPXBDPD5TGXAOQXOIR7","target":"record","payload":{"canonical_record":{"source":{"id":"1612.00974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-03T15:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"a5eb1cca27302fe3ba494a403be37a96b6385e88e8132fa9faf5a2abf96b0603","abstract_canon_sha256":"d157463342d1198adfcd05c2eb1095a93023e724ddedbab088c9c2e2e9b1aefe"},"schema_version":"1.0"},"canonical_sha256":"d89edd0b957dc2378fb335c0e85dc88fe73cbd6996a969667ab3965066c41fee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:53.681377Z","signature_b64":"CUgiDyIuavKurpG8RANtnefhfHaHvCrMA9mFBWONNAPl84o5VsvsCWo1gUQJYccfMQDWbNyC2PlgZBIBlZHpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d89edd0b957dc2378fb335c0e85dc88fe73cbd6996a969667ab3965066c41fee","last_reissued_at":"2026-05-18T00:55:53.680896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:53.680896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.00974","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":"2026-05-18T00:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMu0kJTO00LL7d1VW86YxuUEm9Geu9l7p+g3hGGBrVNyXDtJu3uCf2SC7HmUzh6DzuVIiQNykd3olwJzP3MCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:36:06.995683Z"},"content_sha256":"9950c38d847cad2abca842cf1807d8ef01f20789d78d61803de395d32e561c66","schema_version":"1.0","event_id":"sha256:9950c38d847cad2abca842cf1807d8ef01f20789d78d61803de395d32e561c66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3CPN2C4VPXBDPD5TGXAOQXOIR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Growth factor in $f(T,\\mathcal{T})$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Gabriel Farrugia, Jackson Levi Said","submitted_at":"2016-12-03T15:42:24Z","abstract_excerpt":"We investigate the growth factor for sub-horizon modes during late times in $f(T,\\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\\mathcal{T}$ is the trace of the stress-energy tensor. This is achieved by obtaining the modified M\\'{e}sz\\'{a}ros equation, which describes the evolution of the perturbations of the matter energy density, and obtaining numerical results. Such results are obtained by solving the modified continuity equation and analysing the behaviour of the solutions of the latter using various constraints on the integration constants. Furthermore, the role of the anisot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00974","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":"2026-05-18T00:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dwz2N5xWjRu9hOMMsZ/KuYY1iRQvz4UZwtKISpYXiUWXWYiUqwLHtg8MZTtAMUZCsqbkHdHwKPnREdRIAaKKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:36:06.996038Z"},"content_sha256":"375b341e6beca11b21a4c7617711bb55bee1dad366ef47ba73038df1d33dc55f","schema_version":"1.0","event_id":"sha256:375b341e6beca11b21a4c7617711bb55bee1dad366ef47ba73038df1d33dc55f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/bundle.json","state_url":"https://pith.science/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/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":"2026-06-03T15:36:06Z","links":{"resolver":"https://pith.science/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7","bundle":"https://pith.science/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/bundle.json","state":"https://pith.science/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CPN2C4VPXBDPD5TGXAOQXOIR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3CPN2C4VPXBDPD5TGXAOQXOIR7","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":"d157463342d1198adfcd05c2eb1095a93023e724ddedbab088c9c2e2e9b1aefe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-03T15:42:24Z","title_canon_sha256":"a5eb1cca27302fe3ba494a403be37a96b6385e88e8132fa9faf5a2abf96b0603"},"schema_version":"1.0","source":{"id":"1612.00974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00974","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00974v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00974","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"3CPN2C4VPXBD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3CPN2C4VPXBDPD5T","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3CPN2C4V","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:375b341e6beca11b21a4c7617711bb55bee1dad366ef47ba73038df1d33dc55f","target":"graph","created_at":"2026-05-18T00:55:53Z","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 investigate the growth factor for sub-horizon modes during late times in $f(T,\\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\\mathcal{T}$ is the trace of the stress-energy tensor. This is achieved by obtaining the modified M\\'{e}sz\\'{a}ros equation, which describes the evolution of the perturbations of the matter energy density, and obtaining numerical results. Such results are obtained by solving the modified continuity equation and analysing the behaviour of the solutions of the latter using various constraints on the integration constants. Furthermore, the role of the anisot","authors_text":"Gabriel Farrugia, Jackson Levi Said","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-03T15:42:24Z","title":"Growth factor in $f(T,\\mathcal{T})$ gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00974","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":"sha256:9950c38d847cad2abca842cf1807d8ef01f20789d78d61803de395d32e561c66","target":"record","created_at":"2026-05-18T00:55:53Z","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":"d157463342d1198adfcd05c2eb1095a93023e724ddedbab088c9c2e2e9b1aefe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-03T15:42:24Z","title_canon_sha256":"a5eb1cca27302fe3ba494a403be37a96b6385e88e8132fa9faf5a2abf96b0603"},"schema_version":"1.0","source":{"id":"1612.00974","kind":"arxiv","version":1}},"canonical_sha256":"d89edd0b957dc2378fb335c0e85dc88fe73cbd6996a969667ab3965066c41fee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d89edd0b957dc2378fb335c0e85dc88fe73cbd6996a969667ab3965066c41fee","first_computed_at":"2026-05-18T00:55:53.680896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:53.680896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUgiDyIuavKurpG8RANtnefhfHaHvCrMA9mFBWONNAPl84o5VsvsCWo1gUQJYccfMQDWbNyC2PlgZBIBlZHpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:53.681377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9950c38d847cad2abca842cf1807d8ef01f20789d78d61803de395d32e561c66","sha256:375b341e6beca11b21a4c7617711bb55bee1dad366ef47ba73038df1d33dc55f"],"state_sha256":"f82ac84729c9a9648be1d330df73e54c23989d5808686286639da3f465264513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxynufQKx6gFIM2XFCzR18y3u90Z4ILx6aA0wnNfZC3+NZdCX6fN0uVJOBoe0mYS3CeR6QrbGbpz0DhvqxkjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:36:06.998044Z","bundle_sha256":"8ad116f25ea4a29930ca22361582c5b2ad84393f143c255205306d76879c1fc1"}}