{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HLKHWODSC2FT3LXXDVQZ2KAQWX","short_pith_number":"pith:HLKHWODS","canonical_record":{"source":{"id":"1610.07268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-10-24T02:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"3644da9694b5690e986257d344ddcc23841698ff5247ac1e41fa488721588297","abstract_canon_sha256":"0fa112644092f71e4b780203156363c02618c6cdaad99c461ec0c0f56bcacf62"},"schema_version":"1.0"},"canonical_sha256":"3ad47b3872168b3daef71d619d2810b5fc4b112133b7ebb8a72b5dc817d9e4fa","source":{"kind":"arxiv","id":"1610.07268","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07268","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07268v2","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07268","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"HLKHWODSC2FT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLKHWODSC2FT3LXX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLKHWODS","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HLKHWODSC2FT3LXXDVQZ2KAQWX","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-10-24T02:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"3644da9694b5690e986257d344ddcc23841698ff5247ac1e41fa488721588297","abstract_canon_sha256":"0fa112644092f71e4b780203156363c02618c6cdaad99c461ec0c0f56bcacf62"},"schema_version":"1.0"},"canonical_sha256":"3ad47b3872168b3daef71d619d2810b5fc4b112133b7ebb8a72b5dc817d9e4fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:07.517669Z","signature_b64":"5NCvWJDmnnU/PaAlRMbvFaMTMvlStEAGnjaC7uCVsqylkqBruZDeyvn1i46iIY6jDEQYDOSRYC5kEqIs1bqfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ad47b3872168b3daef71d619d2810b5fc4b112133b7ebb8a72b5dc817d9e4fa","last_reissued_at":"2026-05-18T00:42:07.516933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:07.516933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07268","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ox9ZYK5PPwjft87M5uZyTmN/HQ/DCuCnQOb78RyvK4qnD3UAb7XDXlCzMIC5FVKpGkjcd31LdBx8OsTP0ls0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:23:29.570557Z"},"content_sha256":"873608ceb019ad3f10539f9282f05ed4df91c1a41da203d5b61b6c4498fadc50","schema_version":"1.0","event_id":"sha256:873608ceb019ad3f10539f9282f05ed4df91c1a41da203d5b61b6c4498fadc50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HLKHWODSC2FT3LXXDVQZ2KAQWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Effect of Modified Gravity on the Odds of the Bound Violations of the Turn-Around Radii","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Baojiu Li (Durham Univ.), Jounghun Lee (Seoul Nat'l Univ.)","submitted_at":"2016-10-24T02:51:32Z","abstract_excerpt":"The turn-around radii of the galaxy groups show the imprint of a long battle between their self-gravitational forces and the accelerating space. The standard $\\Lambda$CDM cosmology based on the general relativity (GR) predicts the existence of an upper bound on the expectation value of the turn-around radius which is rarely violated by individual galaxy groups. We speculate that a deviation of the gravitational law from GR on the cosmological scale could cause an appreciable shift of the mean turn-around radius to higher values and make the occurrence of the bound violation more probable. Anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07268","kind":"arxiv","version":2},"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":"2026-05-18T00:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBYozo8ZA4v8Uu9lLHhF7KCUjpSV5dk/hyvcxcAxYmaeoTzKKtlppFCgt/I19QOpwIuC294NvwCIFLCjX/ZhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:23:29.570931Z"},"content_sha256":"314862b7960a1c45214572e878e058dd74d94f3eb7f515335a489254dd179d5a","schema_version":"1.0","event_id":"sha256:314862b7960a1c45214572e878e058dd74d94f3eb7f515335a489254dd179d5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/bundle.json","state_url":"https://pith.science/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/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":"2026-05-28T03:23:29Z","links":{"resolver":"https://pith.science/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX","bundle":"https://pith.science/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/bundle.json","state":"https://pith.science/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLKHWODSC2FT3LXXDVQZ2KAQWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HLKHWODSC2FT3LXXDVQZ2KAQWX","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":"0fa112644092f71e4b780203156363c02618c6cdaad99c461ec0c0f56bcacf62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-10-24T02:51:32Z","title_canon_sha256":"3644da9694b5690e986257d344ddcc23841698ff5247ac1e41fa488721588297"},"schema_version":"1.0","source":{"id":"1610.07268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07268","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07268v2","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07268","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"HLKHWODSC2FT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLKHWODSC2FT3LXX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLKHWODS","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:314862b7960a1c45214572e878e058dd74d94f3eb7f515335a489254dd179d5a","target":"graph","created_at":"2026-05-18T00:42:07Z","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":"The turn-around radii of the galaxy groups show the imprint of a long battle between their self-gravitational forces and the accelerating space. The standard $\\Lambda$CDM cosmology based on the general relativity (GR) predicts the existence of an upper bound on the expectation value of the turn-around radius which is rarely violated by individual galaxy groups. We speculate that a deviation of the gravitational law from GR on the cosmological scale could cause an appreciable shift of the mean turn-around radius to higher values and make the occurrence of the bound violation more probable. Anal","authors_text":"Baojiu Li (Durham Univ.), Jounghun Lee (Seoul Nat'l Univ.)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-10-24T02:51:32Z","title":"The Effect of Modified Gravity on the Odds of the Bound Violations of the Turn-Around Radii"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07268","kind":"arxiv","version":2},"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":"sha256:873608ceb019ad3f10539f9282f05ed4df91c1a41da203d5b61b6c4498fadc50","target":"record","created_at":"2026-05-18T00:42:07Z","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":"0fa112644092f71e4b780203156363c02618c6cdaad99c461ec0c0f56bcacf62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-10-24T02:51:32Z","title_canon_sha256":"3644da9694b5690e986257d344ddcc23841698ff5247ac1e41fa488721588297"},"schema_version":"1.0","source":{"id":"1610.07268","kind":"arxiv","version":2}},"canonical_sha256":"3ad47b3872168b3daef71d619d2810b5fc4b112133b7ebb8a72b5dc817d9e4fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad47b3872168b3daef71d619d2810b5fc4b112133b7ebb8a72b5dc817d9e4fa","first_computed_at":"2026-05-18T00:42:07.516933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:07.516933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5NCvWJDmnnU/PaAlRMbvFaMTMvlStEAGnjaC7uCVsqylkqBruZDeyvn1i46iIY6jDEQYDOSRYC5kEqIs1bqfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:07.517669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:873608ceb019ad3f10539f9282f05ed4df91c1a41da203d5b61b6c4498fadc50","sha256:314862b7960a1c45214572e878e058dd74d94f3eb7f515335a489254dd179d5a"],"state_sha256":"a4440ac94bb305d48b36f249916b4c019ea493e3ba91e586ec0308d962c1fddc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wa00Qm+sfaoDSLrcg3pMBSLA3T/boNZMC4G0OctOMjlR+GOIiu5zb/oirWWqGiDoeKGc4IHCk23liz5fRNOtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:23:29.573094Z","bundle_sha256":"1611d2c067be5c9ddaf88358ccd3ac05eed65fd06b78825843cd4c3d64041f5b"}}