{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VXBK6C6OQC5A4AJSFJIPA66RC5","short_pith_number":"pith:VXBK6C6O","canonical_record":{"source":{"id":"1102.3452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-16T23:05:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6d844bb8e7b63463ca9ef21832b2a9aeab70a4d88533e504df7069103d1a3cd8","abstract_canon_sha256":"ad5c2a3d275b7bd1a3d9dee93f48c8b9de99c1e3cc8e82bcbd61ea7d3469b0bf"},"schema_version":"1.0"},"canonical_sha256":"adc2af0bce80ba0e01322a50f07bd1177ba7bf93dcfccd7f0e86c441374d735a","source":{"kind":"arxiv","id":"1102.3452","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3452","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3452v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3452","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"VXBK6C6OQC5A","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VXBK6C6OQC5A4AJS","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VXBK6C6O","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VXBK6C6OQC5A4AJSFJIPA66RC5","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-16T23:05:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6d844bb8e7b63463ca9ef21832b2a9aeab70a4d88533e504df7069103d1a3cd8","abstract_canon_sha256":"ad5c2a3d275b7bd1a3d9dee93f48c8b9de99c1e3cc8e82bcbd61ea7d3469b0bf"},"schema_version":"1.0"},"canonical_sha256":"adc2af0bce80ba0e01322a50f07bd1177ba7bf93dcfccd7f0e86c441374d735a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:28.985597Z","signature_b64":"8+4GM8y1WJ6XHGOoo/zCUR6ZvXDkV9mu3mu0JOtU1rYVIr2zXFvAjqQy/N4KWId91hbe0dAixLdr2v7nNijrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adc2af0bce80ba0e01322a50f07bd1177ba7bf93dcfccd7f0e86c441374d735a","last_reissued_at":"2026-05-18T04:28:28.985230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:28.985230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3452","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bprYGmsZNAvpnwpUm+SdOiX5p75s+jIcynPythwBvLvTmRipPP/PcYXHlY54FWclrE0VTvZ0LtMAhMKJHfSGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:48:34.826876Z"},"content_sha256":"243edca81b1911d294ffa47cd5af0a5852f874949d90086dc153e4830b69c799","schema_version":"1.0","event_id":"sha256:243edca81b1911d294ffa47cd5af0a5852f874949d90086dc153e4830b69c799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VXBK6C6OQC5A4AJSFJIPA66RC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A free-boundary problem for concrete carbonation: Rigorous justification of the $\\sqrt{{t}}$-law of propagation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Adrian Muntean, Toyohiko Aiki","submitted_at":"2011-02-16T23:05:53Z","abstract_excerpt":"We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. A couple of decades ago, it was observed experimentally that the penetration depth versus time curve (say $s(t)$ vs. $t$) behaves like $s(t)=C\\sqrt{t}$ for sufficiently large times $t > 0$ (with $C$ a positive constant). Consequently, many fitting arguments solely based on this experimental law were used to predict the large-time behavior of carbonation fronts in real structures, a theoretical justification of the $\\sqrt{t}$-law being lacking until"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3452","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGRLIVcEUMexnHxNtdSPdgHeKphvBzqpP1gIk2uyi4cX+ubauLkCD6j9DvGqPzz5jdqZ0xa9cmLpxOdn85H/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:48:34.827228Z"},"content_sha256":"34fccaa7c2b9a39236eafac5b2574fb6c726d300aa0d36c430498478ec979307","schema_version":"1.0","event_id":"sha256:34fccaa7c2b9a39236eafac5b2574fb6c726d300aa0d36c430498478ec979307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/bundle.json","state_url":"https://pith.science/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/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":"2026-06-22T10:48:34Z","links":{"resolver":"https://pith.science/pith/VXBK6C6OQC5A4AJSFJIPA66RC5","bundle":"https://pith.science/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/bundle.json","state":"https://pith.science/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXBK6C6OQC5A4AJSFJIPA66RC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VXBK6C6OQC5A4AJSFJIPA66RC5","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":"ad5c2a3d275b7bd1a3d9dee93f48c8b9de99c1e3cc8e82bcbd61ea7d3469b0bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-16T23:05:53Z","title_canon_sha256":"6d844bb8e7b63463ca9ef21832b2a9aeab70a4d88533e504df7069103d1a3cd8"},"schema_version":"1.0","source":{"id":"1102.3452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3452","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3452v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3452","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"VXBK6C6OQC5A","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VXBK6C6OQC5A4AJS","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VXBK6C6O","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:34fccaa7c2b9a39236eafac5b2574fb6c726d300aa0d36c430498478ec979307","target":"graph","created_at":"2026-05-18T04:28:28Z","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 study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. A couple of decades ago, it was observed experimentally that the penetration depth versus time curve (say $s(t)$ vs. $t$) behaves like $s(t)=C\\sqrt{t}$ for sufficiently large times $t > 0$ (with $C$ a positive constant). Consequently, many fitting arguments solely based on this experimental law were used to predict the large-time behavior of carbonation fronts in real structures, a theoretical justification of the $\\sqrt{t}$-law being lacking until","authors_text":"Adrian Muntean, Toyohiko Aiki","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-16T23:05:53Z","title":"A free-boundary problem for concrete carbonation: Rigorous justification of the $\\sqrt{{t}}$-law of propagation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3452","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":"sha256:243edca81b1911d294ffa47cd5af0a5852f874949d90086dc153e4830b69c799","target":"record","created_at":"2026-05-18T04:28:28Z","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":"ad5c2a3d275b7bd1a3d9dee93f48c8b9de99c1e3cc8e82bcbd61ea7d3469b0bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-16T23:05:53Z","title_canon_sha256":"6d844bb8e7b63463ca9ef21832b2a9aeab70a4d88533e504df7069103d1a3cd8"},"schema_version":"1.0","source":{"id":"1102.3452","kind":"arxiv","version":1}},"canonical_sha256":"adc2af0bce80ba0e01322a50f07bd1177ba7bf93dcfccd7f0e86c441374d735a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adc2af0bce80ba0e01322a50f07bd1177ba7bf93dcfccd7f0e86c441374d735a","first_computed_at":"2026-05-18T04:28:28.985230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.985230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+4GM8y1WJ6XHGOoo/zCUR6ZvXDkV9mu3mu0JOtU1rYVIr2zXFvAjqQy/N4KWId91hbe0dAixLdr2v7nNijrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.985597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:243edca81b1911d294ffa47cd5af0a5852f874949d90086dc153e4830b69c799","sha256:34fccaa7c2b9a39236eafac5b2574fb6c726d300aa0d36c430498478ec979307"],"state_sha256":"911fce0a82c366a84d02e6f5dc16285800991105c44fe2ba37a37f1b2622d035"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBmN/4OUc7FIpJl/JLEyIQONd2WZYVnu0bz01q0wL9DQwgYrnWEYkZXQuULBdZVhkB0nWAZNenLdxXNFUy/mDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:48:34.829148Z","bundle_sha256":"cb45b64da4f283094a0f31b9df4448fe96d1b0831fdcc98290410fb49794a274"}}