{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:24COTTPTCOPRKDQSB2EEBFGSK5","short_pith_number":"pith:24COTTPT","canonical_record":{"source":{"id":"2004.14097","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-04-29T11:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"116346368696da4d8e3550e8d2c04a108951081af684d5dce295c9e994975b98","abstract_canon_sha256":"37aaf3d11f6d9dc2712f18b3cfdcebcc601fd6888a8e874163b9dae262c05853"},"schema_version":"1.0"},"canonical_sha256":"d704e9cdf3139f150e120e884094d2576a8c7c6b7026b8f95033ce6abdc95a92","source":{"kind":"arxiv","id":"2004.14097","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14097","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14097v2","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14097","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"24COTTPTCOPR","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_16","alias_value":"24COTTPTCOPRKDQS","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_8","alias_value":"24COTTPT","created_at":"2026-07-05T00:59:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:24COTTPTCOPRKDQSB2EEBFGSK5","target":"record","payload":{"canonical_record":{"source":{"id":"2004.14097","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-04-29T11:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"116346368696da4d8e3550e8d2c04a108951081af684d5dce295c9e994975b98","abstract_canon_sha256":"37aaf3d11f6d9dc2712f18b3cfdcebcc601fd6888a8e874163b9dae262c05853"},"schema_version":"1.0"},"canonical_sha256":"d704e9cdf3139f150e120e884094d2576a8c7c6b7026b8f95033ce6abdc95a92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:59:25.777071Z","signature_b64":"q+4xci/umdVWEf2WTFVBBw9NdNOF1/qHB1D2KFEVCRyEU9HErxTfOdAS/RApyW1uOOnbkrQnm9nwQBUNXaakAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d704e9cdf3139f150e120e884094d2576a8c7c6b7026b8f95033ce6abdc95a92","last_reissued_at":"2026-07-05T00:59:25.776639Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:59:25.776639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.14097","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":"2026-07-05T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XxlMsjtidtj9Wrc8ZbDF4xAQHHK+CZ2ac239bhr/srR4b8q9a0HBDFZ98hyGT5SV+r2mEZPgdHpsjE8cddTgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:14:58.630239Z"},"content_sha256":"eddaedc70ef1b6463097d49bf653a9bbcd0b24308e74f664881dbaa09a8b8eba","schema_version":"1.0","event_id":"sha256:eddaedc70ef1b6463097d49bf653a9bbcd0b24308e74f664881dbaa09a8b8eba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:24COTTPTCOPRKDQSB2EEBFGSK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the lattice point enumerator via slices and projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Ansgar Freyer, Martin Henk","submitted_at":"2020-04-29T11:41:00Z","abstract_excerpt":"Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question to bound the number of lattice points of a convex body in terms of slices as well as projections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14097","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.14097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGDMxp4rBJKYyB8NlDOkERXq18iSX8+j41b8+BPLKOncY91fadh5F2mpu2ZQNRpZBv6LvDYNz70VFeRnCQ3VBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:14:58.631127Z"},"content_sha256":"988c778df114b36369eaa3f97aab8b7094619d1240f3c81cf7f5926dd6982fb5","schema_version":"1.0","event_id":"sha256:988c778df114b36369eaa3f97aab8b7094619d1240f3c81cf7f5926dd6982fb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24COTTPTCOPRKDQSB2EEBFGSK5/bundle.json","state_url":"https://pith.science/pith/24COTTPTCOPRKDQSB2EEBFGSK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24COTTPTCOPRKDQSB2EEBFGSK5/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":"2026-08-24T04:14:58Z","links":{"resolver":"https://pith.science/pith/24COTTPTCOPRKDQSB2EEBFGSK5","bundle":"https://pith.science/pith/24COTTPTCOPRKDQSB2EEBFGSK5/bundle.json","state":"https://pith.science/pith/24COTTPTCOPRKDQSB2EEBFGSK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24COTTPTCOPRKDQSB2EEBFGSK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:24COTTPTCOPRKDQSB2EEBFGSK5","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":"37aaf3d11f6d9dc2712f18b3cfdcebcc601fd6888a8e874163b9dae262c05853","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-04-29T11:41:00Z","title_canon_sha256":"116346368696da4d8e3550e8d2c04a108951081af684d5dce295c9e994975b98"},"schema_version":"1.0","source":{"id":"2004.14097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14097","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14097v2","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14097","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"24COTTPTCOPR","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_16","alias_value":"24COTTPTCOPRKDQS","created_at":"2026-07-05T00:59:25Z"},{"alias_kind":"pith_short_8","alias_value":"24COTTPT","created_at":"2026-07-05T00:59:25Z"}],"graph_snapshots":[{"event_id":"sha256:988c778df114b36369eaa3f97aab8b7094619d1240f3c81cf7f5926dd6982fb5","target":"graph","created_at":"2026-07-05T00:59:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.14097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question to bound the number of lattice points of a convex body in terms of slices as well as projections.","authors_text":"Ansgar Freyer, Martin Henk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-04-29T11:41:00Z","title":"Bounds on the lattice point enumerator via slices and projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14097","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:eddaedc70ef1b6463097d49bf653a9bbcd0b24308e74f664881dbaa09a8b8eba","target":"record","created_at":"2026-07-05T00:59:25Z","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":"37aaf3d11f6d9dc2712f18b3cfdcebcc601fd6888a8e874163b9dae262c05853","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-04-29T11:41:00Z","title_canon_sha256":"116346368696da4d8e3550e8d2c04a108951081af684d5dce295c9e994975b98"},"schema_version":"1.0","source":{"id":"2004.14097","kind":"arxiv","version":2}},"canonical_sha256":"d704e9cdf3139f150e120e884094d2576a8c7c6b7026b8f95033ce6abdc95a92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d704e9cdf3139f150e120e884094d2576a8c7c6b7026b8f95033ce6abdc95a92","first_computed_at":"2026-07-05T00:59:25.776639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:59:25.776639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q+4xci/umdVWEf2WTFVBBw9NdNOF1/qHB1D2KFEVCRyEU9HErxTfOdAS/RApyW1uOOnbkrQnm9nwQBUNXaakAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:59:25.777071Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.14097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eddaedc70ef1b6463097d49bf653a9bbcd0b24308e74f664881dbaa09a8b8eba","sha256:988c778df114b36369eaa3f97aab8b7094619d1240f3c81cf7f5926dd6982fb5"],"state_sha256":"b9cc8c6d839a868a3e5c8fbbae68b3d4b072d93b8924171a6bc2189e8b477d46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yw+XvSxrHaV5BIHBeKwZrpQ6efaMH7G0SpvLro28ylex4bd1IN1AmTdTLu9BCpEnDGWkoqPo8y9v8xq01sv0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T04:14:58.635880Z","bundle_sha256":"a857ac870f964163475667833f35038d2e5c3be45eb378078e6899c8065c63c2"}}